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A060022 Expansion of (1-x-x^N)/((1-x)(1-x^2)(1-x^3)...(1-x^N)) for N = 3. 8

%I

%S 1,0,1,0,0,-1,-1,-3,-3,-5,-6,-8,-9,-12,-13,-16,-18,-21,-23,-27,-29,

%T -33,-36,-40,-43,-48,-51,-56,-60,-65,-69,-75,-79,-85,-90,-96,-101,

%U -108,-113,-120,-126,-133,-139,-147,-153,-161,-168,-176,-183,-192,-199,-208,-216,-225,-233,-243,-251,-261,-270,-280

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

%C 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

%H Colin Barker, <a href="/A060022/b060022.txt">Table of n, a(n) for n = 0..1000</a>

%H P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s1-17.1.139">Perpetual reciprocants</a>, Proc. London Math. Soc., 17 (1886), 139-151; Coll. Papers II, pp. 584-596.

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).

%F a(n) = A004526(n+2) - A069905(n+2). - _Wesley Ivan Hurt_, Apr 16 2019

%F From _Colin Barker_, Apr 17 2019: (Start)

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

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

%F (End)

%o (PARI) Vec((1 - x - x^3) / ((1 - x)^3*(1 + x)*(1 + x + x^2)) + O(x^40)) \\ _Colin Barker_, Apr 17 2019

%Y Cf. A004526, A069905.

%Y 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).

%K sign,easy

%O 0,8

%A _N. J. A. Sloane_, Mar 17 2001

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Last modified July 23 21:10 EDT 2021. Contains 346265 sequences. (Running on oeis4.)