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A331444
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Number of 2-complete partitions of n with largest part 4.
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2
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0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 6, 9, 11, 14, 18, 23, 27, 33, 39, 47, 54, 63, 72, 84, 94, 107, 120, 136, 150, 168, 185, 206, 225, 248, 270, 297, 321, 350, 378, 411, 441, 477, 511, 551, 588, 631, 672, 720, 764, 815, 864, 920, 972, 1032, 1089, 1154, 1215, 1284, 1350, 1425
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OFFSET
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0,8
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LINKS
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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).
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FORMULA
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G.f.: q^5/qd(4)-q^5/(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) for n>11. - Colin Barker, Jan 27 2020.
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MATHEMATICA
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LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 6, 9, 11}, 60] (* Vincenzo Librandi, Jan 28 2020 *)
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PROG
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(PARI) concat([0, 0, 0, 0, 0, 0], Vec(x^6*(1 + x - x^3 - x^4 + x^5) / ((1 - x)^4*(1 + x)^2*(1 + x^2)*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Jan 27 2020
(MAGMA) I:=[0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 6, 9, 11]; [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
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CROSSREFS
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Cf. A331443.
Sequence in context: A347657 A033069 A022956 * A039865 A304428 A132134
Adjacent sequences: A331441 A331442 A331443 * A331445 A331446 A331447
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Jan 22 2020
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STATUS
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approved
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