A249354 a(n) = n*(3*n^2 + 3*n + 1).

0, 7, 38, 111, 244, 455, 762, 1183, 1736, 2439, 3310, 4367, 5628, 7111, 8834, 10815, 13072, 15623, 18486, 21679, 25220, 29127, 33418, 38111, 43224, 48775, 54782, 61263, 68236, 75719, 83730, 92287, 101408, 111111, 121414, 132335, 143892, 156103, 168986

Offset

0,2

Comments

The series Sum a(n)/A007559(n+1)^3 has the sum 1/9 (cf. A249352), analogous to Sum_{n=1..oo} A000217(n)/A001147(n+1)^2 = 1/8 (cf. A249348 and A249349).

Also, nonnegative numbers m such that 9*m + 1 is a cube. - Bruno Berselli, May 23 2017

Links

Table of n, a(n) for n=0..38.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

G.f.: x*(7+10*x+x^2) / (x-1)^4 . - R. J. Mathar, Oct 28 2014

a(n) = n*A003215(n). - R. J. Mathar, Oct 28 2014

Mathematica

Table[n (3 n^2 + 3 n + 1), {n, 0, 38}] (* or *)
CoefficientList[Series[x (7 + 10 x + x^2)/(x - 1)^4, {x, 0, 38}], x] (* Michael De Vlieger, May 23 2017 *)

Prog

(PARI) A249354(n)=3*n^3+3*n^2+n

Crossrefs

Cf. A132355: numbers m such that 9*m + 1 is a square.

Sequence in context: A165495 A369355 A034858 * A249021 A114290 A277912

Adjacent sequences: A249351 A249352 A249353 * A249355 A249356 A249357

Keyword

nonn,easy

Author

M. F. Hasler, Oct 26 2014

Status

approved