A244243 Number of partitions of n into 7 parts such that every i-th smallest part (counted with multiplicity) is different from i.

1, 7, 22, 48, 88, 140, 207, 291, 389, 508, 646, 809, 995, 1212, 1457, 1742, 2061, 2425, 2833, 3295, 3808, 4386, 5024, 5737, 6522, 7394, 8349, 9406, 10559, 11827, 13208, 14721, 16361, 18153, 20090, 22198, 24472, 26938, 29591, 32462, 35543, 38866, 42427, 46258

Offset

35,2

Links

Alois P. Heinz, Table of n, a(n) for n = 35..1000

Formula

Conjectures from Chai Wah Wu, Apr 18 2024: (Start)

a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-7) - a(n-8) + a(n-10) + a(n-11) + 2*a(n-12) - 2*a(n-16) - a(n-17) - a(n-18) + a(n-20) + a(n-21) + a(n-23) - a(n-26) - a(n-27) + a(n-28) for n > 77.

G.f.: x^35*(-x^42 + 2*x^36 + 2*x^35 + 2*x^34 + 2*x^33 + 4*x^32 + x^31 + 2*x^30 - 3*x^29 - 8*x^28 - 14*x^27 - 25*x^26 - 24*x^25 - 16*x^24 + 4*x^23 + 29*x^22 + 50*x^21 + 58*x^20 + 56*x^19 + 28*x^18 - 8*x^17 - 47*x^16 - 75*x^15 - 76*x^14 - 60*x^13 - 28*x^12 + 10*x^11 + 42*x^10 + 55*x^9 + 53*x^8 + 33*x^7 + 14*x^6 - 5*x^5 - 18*x^4 - 19*x^3 - 14*x^2 - 6*x - 1)/(x^28 - x^27 - x^26 + x^23 + x^21 + x^20 - x^18 - x^17 - 2*x^16 + 2*x^12 + x^11 + x^10 - x^8 - x^7 - x^5 + x^2 + x - 1). (End)

Crossrefs

Column k=7 of A238406.

Sequence in context: A197059 A331229 A299283 * A223833 A014073 A288114

Adjacent sequences: A244240 A244241 A244242 * A244244 A244245 A244246

Keyword

nonn,changed

Author

Alois P. Heinz, Jun 23 2014

Status

approved