A016861 a(n) = 5*n + 1.

1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, 81, 86, 91, 96, 101, 106, 111, 116, 121, 126, 131, 136, 141, 146, 151, 156, 161, 166, 171, 176, 181, 186, 191, 196, 201, 206, 211, 216, 221, 226, 231, 236, 241, 246, 251, 256, 261, 266, 271, 276, 281

Offset

0,2

Comments

Numbers ending in 1 or 6.

Apart from initial terms, same as 5n-14.

Complement of A047203; A027445(a(n)) mod 10 = 4. - Reinhard Zumkeller, Oct 23 2006

Campbell reference shows: "A graph on n vertices with at least 4n-9 edges is intrinsically linked. A graph on n vertices with at least 5n-14 edges is intrinsically knotted." - Jonathan Vos Post, Jan 18 2007

Central terms of the triangle in A153125: a(n) = A153125(2*n+1, n+1). - Reinhard Zumkeller, Dec 20 2008

For n > 2, also the number of (not necessarily maximal) cliques in the n-Moebius ladder graph. - Eric W. Weisstein, Nov 29 2017

For n > 3, also the number of (not necessarily maximal) cliques in the n-prism graph. - Eric W. Weisstein, Nov 29 2017

For n >= 1, a(n) is the size of any hexagonal chain graph with n cells. - Christian Barrientos, Sarah Minion, Mar 07 2018

For n >= 1, a(n) is the number of possible outcomes of the summation when using n dice. - Bram Kole, Dec 24 2018

Numbers congruent to 1 (mod 5). - Muniru A Asiru, Jan 01 2019

Numbers k such that the k-th Fibonacci number, A000045(k), and the k-th Lucas number, A000032(k), end with the same decimal digit. - Amiram Eldar, Apr 15 2023

Links

Ivan Panchenko, Table of n, a(n) for n = 0..1000

J. Campbell, T. W. Mattman, R. Ottman, J. Pyzer, M. Rodrigues and S. Williams, Intrinsic knotting and linking of almost complete graphs, arXiv:math/0701422 [math.GT], Jan 15 2007.

Tanya Khovanova, Recursive Sequences.

Eric Weisstein's World of Mathematics, Clique.

Eric Weisstein's World of Mathematics, Moebius Ladder.

Eric Weisstein's World of Mathematics, Prism Graph.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

G.f.: (1+4*x)/(1-x)^2.

Row sums of triangle A131843. - Gary W. Adamson, Jul 21 2007

a(n) = 2*a(n-1) - a(n-2) with a(0)=1, a(1)=6. - Vincenzo Librandi, Aug 01 2010

a(n) = A017293(n)/2 = A008587(n)+1. - Wesley Ivan Hurt, May 03 2014

E.g.f.: exp(x)*(1 + 5*x). - Stefano Spezia, Mar 23 2021

Sum_{n>=0} (-1)^n/a(n) = sqrt(2+2/sqrt(5))*Pi/10 + log(phi)/sqrt(5) + log(2)/5, where phi is the golden ratio (A001622). - Amiram Eldar, Apr 15 2023

Maple

A016861:=n->5*n+1; seq(A016861(n), n=0..100); # Wesley Ivan Hurt, May 03 2014

Mathematica

Range[1, 500, 5] (* Vladimir Joseph Stephan Orlovsky, May 26 2011 *)
LinearRecurrence[{2, -1}, {6, 11}, {0, 20}] (* Eric W. Weisstein, Nov 29 2017 *)
CoefficientList[Series[(1 + 4 x)/(-1 + x)^2, {x, 0, 20}], x] (* Eric W. Weisstein, Nov 29 2017 *)

Prog

(Haskell)
a016861 = (+ 1) . (* 5)
a016861_list = [1, 6 ..]  -- Reinhard Zumkeller, Jun 16 2013
(PARI) a(n)=5*n+1 \\ Charles R Greathouse IV, Jul 10 2016
(GAP) a:=List([0..60], n->5*n+1);; Print(a); # Muniru A Asiru, Jan 01 2019

Crossrefs

Cf. A093562 ((5, 1) Pascal, column m=1).

Cf. A000566 (partial sums).

Cf. A000032, A000045, A001622, A131843, A342819.

Sequence in context: A315466 A299977 A145287 * A140232 A315467 A315468

Adjacent sequences: A016858 A016859 A016860 * A016862 A016863 A016864

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 11 1996

Extensions

More terms from Reinhard Zumkeller, Oct 23 2006

Status

approved