A003949 Expansion of g.f. (1+x)/(1-6*x).

1, 7, 42, 252, 1512, 9072, 54432, 326592, 1959552, 11757312, 70543872, 423263232, 2539579392, 15237476352, 91424858112, 548549148672, 3291294892032, 19747769352192, 118486616113152, 710919696678912, 4265518180073472, 25593109080440832, 153558654482644992

Offset

0,2

Comments

Coordination sequence for infinite tree with valency 7.

For n >= 1, a(n+1) is equal to the number of functions f:{1,2,...,n+1}->{1,2,3,4,5,6,7} such that for fixed, different x_1, x_2,...,x_n in {1,2,...,n+1} and fixed y_1, y_2,...,y_n in {1,2,3,4,5,6,7} we have f(x_i)<>y_i, (i=1,2,...,n). - Milan Janjic, May 10 2007

For n >= 1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,2,3,5,6} with no two adjacent letters identical. - Milan Janjic, Jan 31 2015

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 308

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Index to divisibility sequences

Index entries for linear recurrences with constant coefficients, signature (6).

Index entries for sequences related to trees

Formula

G.f.: (1+x)/(1-6*x).

a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 5. - Philippe Deléham, Jul 10 2005

a(0)=1; for n > 0, a(n) = 7*6^(n-1). - Vincenzo Librandi, Nov 18 2010

a(0)=1, a(1)=7, a(n) = 6*a(n-1). - Vincenzo Librandi, Dec 10 2012

E.g.f.: (7*exp(6*x) - 1)/6. - G. C. Greubel, Sep 24 2019

Maple

k:=7; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by G. C. Greubel, Sep 24 2019

Mathematica

q = 7; Join[{a = 1}, Table[If[n != 0, a = q*a - a, a = q*a], {n, 0, 25}]] (* or *) Join[{1}, 7*6^Range[0, 25]] (* Vladimir Joseph Stephan Orlovsky, Jul 11 2011 *)
CoefficientList[Series[(1+x)/(1-6*x), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 10 2012 *)

Prog

(PARI) a(n)=if(n, 7*6^(n-1), 1) \\ Charles R Greathouse IV, Mar 22 2016
(Magma) k:=7; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // G. C. Greubel, Sep 24 2019
(Magma) R<x>:=PowerSeriesRing(Rationals(), 25); Coefficients(R!( (1+x)/(1-6*x))); // Marius A. Burtea, Jan 20 2020
(Sage) k=7; [1]+[k*(k-1)^(n-1) for n in (1..25)] # G. C. Greubel, Sep 24 2019
(GAP) k:=7;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # G. C. Greubel, Sep 24 2019

Crossrefs

Cf. A003947, A003948, A003950, A003951.

Sequence in context: A170592 A170640 A170688 * A252700 A033133 A082035

Adjacent sequences: A003946 A003947 A003948 * A003950 A003951 A003952

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Edited by N. J. A. Sloane, Dec 04 2009

Status

approved