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 A331443 Number of 1-complete partitions of n with largest part 4. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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 * A035946 A303939 A326446 Adjacent sequences:  A331440 A331441 A331442 * A331444 A331445 A331446 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Jan 22 2020 STATUS approved

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Last modified May 22 06:54 EDT 2022. Contains 353933 sequences. (Running on oeis4.)