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

0,2

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).

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

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 *)

Prog

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

Crossrefs

Cf. A082109.

Sequence in context: A035329 A097973 A038644 * A230651 A184457 A184449

Adjacent sequences: A083076 A083077 A083078 * A083080 A083081 A083082

Keyword

easy,nonn

Author

Paul Barry, Apr 23 2003

Status

approved