A060022 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 3.

1, 0, 1, 0, 0, -1, -1, -3, -3, -5, -6, -8, -9, -12, -13, -16, -18, -21, -23, -27, -29, -33, -36, -40, -43, -48, -51, -56, -60, -65, -69, -75, -79, -85, -90, -96, -101, -108, -113, -120, -126, -133, -139, -147, -153, -161, -168, -176, -183, -192, -199, -208, -216, -225, -233, -243, -251, -261, -270, -280

Offset: 0

Author

N. J. A. Sloane, Mar 17 2001

Keywords

• sign
• easy

Comments

Difference between the number of partitions of n+2 into 2 parts and the number of partitions of n+2 into 3 parts. - Wesley Ivan Hurt, Apr 16 2019

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• P. A. MacMahon, Perpetual reciprocants, Proc. London Math. Soc., 17 (1886), 139-151; Coll. Papers II, pp. 584-596.
• Index entries for sequences related to partitions
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,-1,-1,1).

Crossrefs

Cf. A004526, A069905.

Cf. For other values of N: this sequence (N=3), A060023 (N=4), A060024 (N=5), A060025 (N=6), A060026 (N=7), A060027 (N=8), A060028 (N=9), A060029 (N=10).

Programs

PARI

Vec((1 - x - x^3) / ((1 - x)^3*(1 + x)*(1 + x + x^2)) + O(x^40)) \\ Colin Barker, Apr 17 2019

Formula

a(n) = A004526(n+2) - A069905(n+2). - Wesley Ivan Hurt, Apr 16 2019

From Colin Barker, Apr 17 2019: (Start)

G.f.: (1 - x - x^3) / ((1 - x)^3*(1 + x)*(1 + x + x^2)).

a(n) = a(n-1) + a(n-2) - a(n-4) - a(n-5) + a(n-6) for n>5.

(End)