A244242 Number of partitions of n into 6 parts such that every i-th smallest part (counted with multiplicity) is different from i.

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

Offset

27,2

Links

Alois P. Heinz, Table of n, a(n) for n = 27..1000

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

Adjacent sequences: A244239 A244240 A244241 * A244243 A244244 A244245

Keyword

nonn

Author

Alois P. Heinz, Jun 23 2014

Status

approved