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A244242 Number of partitions of n into 6 parts such that every i-th smallest part (counted with multiplicity) is different from i. 2
1, 6, 16, 31, 52, 76, 107, 143, 184, 233, 289, 354, 427, 512, 606, 716, 835, 972, 1122, 1292, 1476, 1685, 1909, 2161, 2432, 2734, 3057, 3417, 3799, 4222, 4673, 5168, 5693, 6270, 6879, 7545, 8249, 9014, 9821, 10698, 11619, 12616, 13665, 14795, 15981, 17259 (list; graph; refs; listen; history; text; internal format)
OFFSET
27,2
LINKS
FORMULA
Conjectures from Chai Wah Wu, Apr 18 2024: (Start)
a(n) = a(n-1) + a(n-2) - a(n-5) - 2*a(n-7) + a(n-9) + a(n-10) + a(n-11) + a(n-12) - 2*a(n-14) - a(n-16) + a(n-19) + a(n-20) - a(n-21) for n > 57.
G.f.: x^27*(-x^30 + 2*x^25 + 2*x^24 + 2*x^23 + 4*x^22 + 2*x^21 + x^20 - 9*x^19 - 12*x^18 - 16*x^17 - 12*x^16 + x^15 + 13*x^14 + 24*x^13 + 25*x^12 + 20*x^11 + 3*x^10 - 11*x^9 - 23*x^8 - 22*x^7 - 15*x^6 - 6*x^5 + 5*x^4 + 9*x^3 + 9*x^2 + 5*x + 1)/((x - 1)^6*(x + 1)^3*(x^2 + 1)*(x^2 - x + 1)*(x^2 + x + 1)^2*(x^4 + x^3 + x^2 + x + 1)). (End)
CROSSREFS
Column k=6 of A238406.
Sequence in context: A115007 A005891 A108182 * A092286 A301723 A288113
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 23 2014
STATUS
approved

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Last modified May 22 09:32 EDT 2024. Contains 372745 sequences. (Running on oeis4.)