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A094909 Let p_k(n) = number of partitions of n into exactly k parts; sequence gives p_3(n-3) + p_2(n-2) + 1.

%I A094909 #13 Nov 15 2019 08:00:47
%S A094909 1,1,1,1,2,2,4,4,6,7,9,10,13,14,17,19,22,24,28,30,34,37,41,44,49,52,
%T A094909 57,61,66,70,76,80,86,91,97,102,109,114,121,127,134,140,148,154,162,
%U A094909 169,177,184,193,200,209,217,226,234,244,252,262,271,281,290,301,310,321
%N A094909 Let p_k(n) = number of partitions of n into exactly k parts; sequence gives p_3(n-3) + p_2(n-2) + 1.
%H A094909 S. L. Devadoss, <a href="http://www.ams.org/notices/200406/fea-devadoss.pdf">Combinatorial equivalence of real moduli spaces</a>, Notices Amer. Math. Soc., 51 (No. 6, 2004), 620-628 (see Cor. 7).
%H A094909 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,-1,-1,1).
%F A094909 G.f.: (x^7-x^6-x^5-x^4+x^3+x^2-1)/((1+x)*(x^2+x+1)*(x-1)^3). - _Alois P. Heinz_, Jul 19 2015
%F A094909 72*a(n) = 8*A099837(n+3) +27*(-1)^n +29 +6*n^2, (n>1). - _R. J. Mathar_, Nov 15 2019
%o A094909 (PARI) Vec((x^7-x^6-x^5-x^4+x^3+x^2-1)/((1+x)*(x^2+x+1)*(x-1)^3) + O(x^80)) \\ _Michel Marcus_, Jul 19 2015
%Y A094909 p_k(n) = A008284(n,k).
%K A094909 nonn,easy
%O A094909 0,5
%A A094909 _N. J. A. Sloane_, Jun 18 2004
%E A094909 a(0)=1 prepended by _Alois P. Heinz_, Jul 19 2015