A115565 a(n) = 5*n^4 - 10*n^3 + 20*n^2 - 15*n + 11.

11, 61, 281, 911, 2311, 4961, 9461, 16531, 27011, 41861, 62161, 89111, 124031, 168361, 223661, 291611, 374011, 472781, 589961, 727711, 888311, 1074161, 1287781, 1531811, 1809011, 2122261, 2474561, 2869031, 3308911, 3797561, 4338461, 4935211, 5591531

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Formula

a(1-n) = a(n) = 5*(n^2-n)^2 +15*(n^2-n) +11. - Michael Somos, May 15 2006

a(1)=11, a(2)=61, a(3)=281, a(4)=911, a(5)=2311, a(n)=5*a(n-1)-10*a(n-2)+ 10*a(n-3)-5*a(n-4)+a(n-5). - Harvey P. Dale, Oct 03 2011

G.f.: x*(11+6*x+86*x^2+6*x^3+11*x^4)/(1-x)^5. - Wesley Ivan Hurt, Aug 22 2015

Maple

A115565:=n->5*n^4 - 10*n^3 + 20*n^2 - 15*n + 11: seq(A115565(n), n=1..40); # Wesley Ivan Hurt, Aug 22 2015

Mathematica

Table[5n^4-10n^3+20n^2-15n+11, {n, 40}] (* or *) LinearRecurrence[ {5, -10, 10, -5, 1}, {11, 61, 281, 911, 2311}, 40] (* Harvey P. Dale, Oct 03 2011 *)
CoefficientList[Series[(11 + 6 x + 86 x^2 + 6 x^3 + 11 x^4)/(1 - x)^5, {x, 0, 40}], x] (* Wesley Ivan Hurt, Aug 22 2015 *)

Prog

ay1[1] := 11; a[1] :=50; b[1] :=170; c[1] :=240; k := 120; Repeat ay1[1] := ay1[1] + a[1]; a[1] := a[1] + b[1]; b[1] := b[1] + c[1]; c[1] := c[1] + k; writeln(ay1[1]); Until 1 < 0;
(Magma) [5*(n^2-n)^2 +15*(n^2-n) +11: n in [1..40]]; // Vincenzo Librandi, Oct 04 2011
(PARI) a(n) = 5*n^4 - 10*n^3 + 20*n^2 - 15*n + 11 \\ Charles R Greathouse IV, Aug 22 2015
(PARI) first(m)=vector(m, i, 5*i^4 - 10*i^3 + 20*i^2 - 15*i + 11) \\ Anders Hellström, Aug 22 2015

Crossrefs

Sequence in context: A023298 A320145 A106992 * A137410 A268863 A199414

Adjacent sequences: A115562 A115563 A115564 * A115566 A115567 A115568

Keyword

nonn,easy

Author

Aldrich Stevens (Aldrichstevens(AT)msn.com), Mar 11 2006

Extensions

Checked by N. J. A. Sloane, Mar 29 2006

Edited by N. J. A. Sloane, Jun 13 2008

Status

approved