A185395 a(3n) = n^2, a(3n+1) = a(3n+2) = 3*n*(n+1)/2.

0, 0, 0, 1, 3, 3, 4, 9, 9, 9, 18, 18, 16, 30, 30, 25, 45, 45, 36, 63, 63, 49, 84, 84, 64, 108, 108, 81, 135, 135, 100, 165, 165, 121, 198, 198, 144, 234, 234, 169, 273, 273, 196, 315, 315, 225, 360, 360, 256

Offset

0,5

Comments

Expansion of ((x+x^2)/(1-x^3))^k with k = 3 ; for k = 1 see A011655, for k = 2 see A186731, for k = 4 see A185292.

Column k = 3 of triangle in A198295.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-3,0,0,1).

Formula

G.f.: (x*(1+x)/(1-x^3))^3.

Mathematica

LinearRecurrence[{0, 0, 3, 0, 0, -3, 0, 0, 1}, {0, 0, 0, 1, 3, 3, 4, 9, 9}, 50] (* Harvey P. Dale, Jan 23 2013 *)

Prog

(PARI) x='x+O('x^50); concat([0, 0, 0], Vec((x*(1+x)/(1-x^3))^3)) \\ G. C. Greubel, Jun 29 2017

Crossrefs

Cf. A000217, A000290, A011655, A045943, A186731, A185292, A198295.

Sequence in context: A183501 A086239 A016605 * A060372 A128036 A332311

Adjacent sequences: A185392 A185393 A185394 * A185396 A185397 A185398

Keyword

easy,nonn

Author

Philippe Deléham, Jan 21 2012

Status

approved