A083079 4th column of number array A083075.

1, 63, 229, 547, 1065, 1831, 2893, 4299, 6097, 8335, 11061, 14323, 18169, 22647, 27805, 33691, 40353, 47839, 56197, 65475, 75721, 86983, 99309, 112747, 127345, 143151, 160213, 178579, 198297, 219415, 241981, 266043, 291649, 318847, 347685

Offset: 0

Author

Paul Barry, Apr 23 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A082109.

Programs

Magma

[8*n^3+28*n^2+26*n+1: n in [0..30]]; // Vincenzo Librandi, Nov 12 2011

Mathematica

Table[8 n^3 + 28 n^2 + 26 n + 1, {n, 0, 40}] (* or *) LinearRecurrence[ {4,-6,4,-1},{1,63,229,547},40] (* Harvey P. Dale, May 14 2011 *)

Formula

a(n) = 8*n^3 + 28*n^2 + 26*n + 1 = (n*(2n+3)^3 + 1)/(n+1).

G.f.: (1 + 59*x - 17*x^2 + 5*x^3)/(1-x)^4. - Harvey P. Dale, May 14 2011

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4); a(0)=1, a(1)=63, a(2)=229, a(3)=547. - Harvey P. Dale, May 14 2011