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A244241
Number of partitions of n into 5 parts such that every i-th smallest part (counted with multiplicity) is different from i.
2
1, 5, 11, 19, 29, 39, 53, 67, 84, 103, 126, 150, 179, 210, 246, 285, 329, 376, 430, 487, 551, 619, 695, 775, 864, 958, 1061, 1170, 1289, 1414, 1551, 1694, 1849, 2012, 2188, 2372, 2570, 2777, 2999, 3231, 3479, 3737, 4013, 4300, 4605, 4923, 5260, 5610, 5981
OFFSET
20,2
LINKS
FORMULA
Conjectures from Chai Wah Wu, Apr 18 2024: (Start)
a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-6) - a(n-7) + a(n-8) + a(n-9) + a(n-10) - a(n-13) - a(n-14) + a(n-15) for n > 40.
G.f.: x^20*(-x^20 + 2*x^16 + 2*x^15 + 4*x^14 + x^13 - 3*x^12 - 7*x^11 - 9*x^10 - 5*x^9 + 2*x^8 + 8*x^7 + 9*x^6 + 8*x^5 + x^4 - 3*x^3 - 5*x^2 - 4*x - 1)/((x - 1)^5*(x + 1)^2*(x^2 + 1)*(x^2 + x + 1)*(x^4 + x^3 + x^2 + x + 1)). (End)
CROSSREFS
Column k=5 of A238406.
Sequence in context: A141158 A239732 A130828 * A108151 A209188 A356247
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 23 2014
STATUS
approved