A331443 Number of 1-complete partitions of n with largest part 4.

0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 5, 8, 10, 14, 16, 22, 26, 32, 37, 46, 52, 62, 70, 82, 92, 106, 117, 134, 148, 166, 182, 204, 222, 246, 267, 294, 318, 348, 374, 408, 438, 474, 507, 548, 584, 628, 668, 716, 760, 812, 859, 916, 968, 1028, 1084, 1150, 1210, 1280, 1345, 1420

Offset

0,8

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Seung Kyung Park, The r-complete partitions, Discrete mathematics 183.1-3 (1998): 293-297.

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-2,0,0,1,1,-1).

Formula

G.f.: q^5/qd(4)-q^5/((1-q^4)*(1-q^3))-q^6/(1-q^4) where qd(k) = Product_{i=1..k} (1-q^i).

a(n) = a(n-1) + a(n-2) - 2*a(n-5) + a(n-8) + a(n-9) - a(n-10). - Colin Barker, Jan 27 2020

Mathematica

LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 5, 8, 10}, 60] (* Vincenzo Librandi, Jan 28 2020 *)

Prog

concat([0, 0, 0, 0, 0, 0, 0], Vec(x^7*(2 - x^3 - x^4 + x^5) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)) + O(x^60))) \\ Colin Barker, Jan 27 2020
(Magma) I:=[0, 0, 0, 0, 0, 0, 0, 2, 2, 4, 5, 8, 10]; [n le 13 select I[n] else  Self(n-1) + Self(n-2) - 2*Self(n-5) + Self(n-8) + Self(n-9) - Self(n-10): n in [1..60]]; // Vincenzo Librandi, Jan 28 2020

Crossrefs

Cf. A331444.

Sequence in context: A317810 A308954 A053097 * A367411 A367684 A035946

Adjacent sequences: A331440 A331441 A331442 * A331444 A331445 A331446

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 22 2020

Status

approved