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A276235
Number of triangular partitions of n of order 6.
4
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
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
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 29 2016
STATUS
approved