A244241 Number of partitions of n into 5 parts such that every i-th smallest part (counted with multiplicity) is different from i.

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

Alois P. Heinz, Table of n, a(n) for n = 20..1000

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

Adjacent sequences: A244238 A244239 A244240 * A244242 A244243 A244244

Keyword

nonn,changed

Author

Alois P. Heinz, Jun 23 2014

Status

approved