A008354 a(n) = (5*n^2 + 1)*n^2 / 6.

0, 1, 14, 69, 216, 525, 1086, 2009, 3424, 5481, 8350, 12221, 17304, 23829, 32046, 42225, 54656, 69649, 87534, 108661, 133400, 162141, 195294, 233289, 276576, 325625, 380926, 442989, 512344, 589541, 675150, 769761, 873984, 988449, 1113806, 1250725, 1399896

Offset: 0

Author

N. J. A. Sloane and J. H. Conway

Keywords

• nonn
• easy

Comments

Partial sums of A005902. - Jonathan Vos Post, Mar 14 2006

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

Crossrefs

Cf. A005901, A005902.

Programs

GAP

List([0..30], n -> (5*n^2+1)*n^2/6); # Muniru A Asiru, Feb 12 2018

Maple

a:= n-> 5*n^4/6 + n^2/6: seq(a(n), n=0..45);

Mathematica

Table[n^2 (5 n^2 + 1)/6, {n, 0, 30}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 14, 69, 216}, 30] (* Harvey P. Dale, Feb 12 2015 *)

Formula

From R. J. Mathar, Aug 10 2008: (Start)

O.g.f.: x*(1 + x)*(x^2 + 8*x + 1)/(1 - x)^5.

a(n) = n*A004068(n). (End)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4, a(0)=0, a(1)=1, a(2)=14, a(3)=69, a(4)=216. - Harvey P. Dale, Feb 12 2015

Extensions

Definition corrected by R. J. Mathar, Aug 10 2008