1,1

Andrew Howroyd, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (12,-35,-38,192,245, -1925,3935,-2577,366,-5966, 6996,3981,-10122,8449,6980, -26762,28077,-27459,30799,-24399, 13818,-6052,1940,-406, -376,496,-192,24).

G.f.: x*(2 - 11*x - 20*x^2 + 136*x^3 + 92*x^4 - 1030*x^5 + 1579*x^6 + 623*x^7 - 4928*x^8 + 1604*x^9 + 1160*x^10 + 14400*x^11 - 19692*x^12 + 6655*x^13 + 12644*x^14 - 38248*x^15 + 43316*x^16 - 48148*x^17 + 61499*x^18 - 51379*x^19 + 30810*x^20 - 15812*x^21 + 6524*x^22 - 2002*x^23 - 770*x^24 + 1392*x^25 - 548*x^26 + 64*x^27)/((1 - x)*(1 - 5*x - 8*x^2 + 5*x^3 + 10*x^4 + x^5 - 3*x^6 - 4*x^7 + 2*x^8)*(1 - 6*x + 2*x^2 + 19*x^3 + x^4 - 169*x^5 + 607*x^6 - 913*x^7 + 1279*x^8 - 2352*x^9 + 3003*x^10 - 3418*x^11 + 2775*x^12 - 1279*x^13 + 676*x^14 - 156*x^15 + 4*x^16 + 62*x^17 - 60*x^18 + 12*x^19)).

a(n) = 1 + A180763(n) + A230814(n) / 2.

The a(2) = 13 partitions are:

1 1 1 1 1 1 1 2 1 1 2 1 1 2 1 1 2 1

1 1 1 2 2 2 1 2 1 1 2 2 2 1 2 2 2 1

.

1 1 2 1 1 2 1 1 2 1 2 2 1 2 2 1 2 2 1 2 3

2 1 1 2 1 2 2 2 1 1 2 1 2 1 1 2 2 1 3 2 1

Row 3 of A391824.

Cf. A180763, A230814, A391826.

Sequence in context: A160459 A037752 A037640 * A137967 A045764 A106999

Adjacent sequences: A391824 A391825 A391826 * A391828 A391829 A391830

Andrew Howroyd, Jan 10 2026

approved