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A053801
Number of basis partitions of n+36 with Durfee square size 6.
2
1, 2, 4, 8, 14, 24, 40, 62, 94, 140, 202, 286, 398, 542, 728, 966, 1262, 1630, 2084, 2634, 3300, 4100, 5048, 6170, 7490, 9028, 10816, 12884, 15258, 17978, 21082, 24602, 28586, 33080, 38124, 43776, 50090, 57114, 64916, 73560, 83104, 93626
OFFSET
0,2
LINKS
M. D. Hirschhorn, Basis partitions and Rogers-Ramanujan partitions, Discrete Math. 205 (1999), 241-243.
Index entries for linear recurrences with constant coefficients, signature (3,-3,3,-6,7,-6,6,-6,7,-6,3,-3,3,-1).
FORMULA
Euler transform of length 12 sequence [ 2, 1, 2, 1, 2, 1, 0, -1, 0, -1, 0, -1]. - Michael Somos, Sep 02 2006
G.f.: (1+q)(1+q^2)(1+q^3)(1+q^4)(1+q^5)(1+q^6)/((1-q)(1-q^2)(1-q^3)(1-q^4)(1-q^5)(1-q^6)).
a(n) = 3*a(n-1) - 3*a(n-2) + 3*a(n-3) - 6*a(n-4) + 7*a(n-5) - 6*a(n-6) + 6*a(n-7) - 6*a(n-8) + 7*a(n-9) - 6*a(n-10) + 3*a(n-11) - 3*a(n-12) + 3*a(n-13) - a(n-14) for n>14. - Colin Barker, Jan 02 2020
PROG
(PARI) {a(n)=if(n<0, 0, polcoeff( prod(k=1, 6, (1+x^k)/(1-x^k), 1+x*O(x^n)), n))} /* Michael Somos, Sep 02 2006 */
(PARI) Vec((1 + x^2)*(1 - x + x^2 - x^3 + x^4)*(1 - x^2 + x^4)*(1 + x^4) / ((1 - x)^6*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^50)) \\ Colin Barker, Jan 02 2020
CROSSREFS
Sequence in context: A280874 A243815 A060046 * A091778 A053802 A091779
KEYWORD
easy,nonn
AUTHOR
James A. Sellers, Mar 27 2000
STATUS
approved