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

Author

Alois P. Heinz, Jun 23 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 35..1000
• N. Guru Sharan and Armin Straub, Partitions with Durfee triangles of fixed size, arXiv:2507.19047 [math.CO], 2025. See p. 5.

Crossrefs

Column k=7 of A238406.

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)