A276235 Number of triangular partitions of n of order 6.

1, 6, 21, 61, 156, 361, 781, 1599, 3124, 5876, 10696, 18917, 32627, 55027, 90948, 147604, 235610, 370395, 574181, 878616, 1328343, 1985833, 2937727, 4303249, 6245316, 8984932, 12819913, 18149148, 25503623, 35586130, 49321916, 67922649, 92967170, 126503102

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

L. Carlitz, R. Scoville, A generating function for triangular partitions, Math. Comp. 29 (1975) 67-77.

Index entries for linear recurrences with constant coefficients, signature (6, -15, 25, -45, 85, -135, 198, -298, 442, -627, 856, -1156, 1560, -2048, 2614, -3322, 4201, -5209, 6349, -7697, 9268, -11004, 12899, -15023, 17404, -19943, 22592, -25456, 28539, -31676, 34828, -38103, 41461, -44737, 47875, -50957, 53980, -56736, 59150, -61376, 63385, -64954, 66068, -66888, 67385, -67385, 66888, -66068, 64954, -63385, 61376, -59150, 56736, -53980, 50957, -47875, 44737, -41461, 38103, -34828, 31676, -28539, 25456, -22592, 19943, -17404, 15023, -12899, 11004, -9268, 7697, -6349, 5209, -4201, 3322, -2614, 2048, -1560, 1156, -856, 627, -442, 298, -198, 135, -85, 45, -25, 15, -6, 1).

Formula

G.f.: 1/((1-x)^6*(1-x^3)^5*(1-x^5)^4*(1-x^7)^3*(1-x^9)^2* (1-x^11)).

Mathematica

CoefficientList[Series[1/((1 - x)^6 (1 - x^3)^5 (1 - x^5)^4 (1 - x^7)^3 (1 - x^9)^2 (1 - x^11)), {x, 0, 50}], x]

Prog

(Magma) m:=50; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-x)^6*(1-x^3)^5*(1-x^5)^4*(1-x^7)^3*(1-x^9)^2*(1-x^11))));
(PARI) Vec(1/((1-x)^6*(1-x^3)^5*(1-x^5)^4*(1-x^7)^3*(1-x^9)^2*(1-x^11)) + O(x^30)) \\ Felix Fröhlich, Aug 29 2016

Crossrefs

Cf. number of triangular partitions of n of order k: A000012 (k=1), A001840 (k=2), A084439 (k=3). A084446 (k=4), A084447 (k=5), this sequence (k=6), A276236 (k=7), A276279 (k=8), A276280 (k=9).

Sequence in context: A113070 A009147 A012593 * A334833 A048476 A122678

Adjacent sequences: A276232 A276233 A276234 * A276236 A276237 A276238

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 29 2016

Status

approved