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%I #27 Sep 08 2022 08:46:25
%S 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,
%T 120,136,150,168,185,206,225,248,270,297,321,350,378,411,441,477,511,
%U 551,588,631,672,720,764,815,864,920,972,1032,1089,1154,1215,1284,1350,1425
%N Number of 2-complete partitions of n with largest part 4.
%H Colin Barker, <a href="/A331444/b331444.txt">Table of n, a(n) for n = 0..1000</a>
%H Seung Kyung Park, <a href="https://doi.org/10.1016/S0012-365X(97)00177-5">The r-complete partitions</a>, Discrete mathematics 183.1-3 (1998): 293-297.
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-2,0,0,1,1,-1).
%F G.f.: q^5/qd(4)-q^5/(1-q^4) where qd(k) = Product_{i=1..k} (1-q^i).
%F 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.
%t 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 *)
%o (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
%o (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
%Y Cf. A331443.
%K nonn,easy
%O 0,8
%A _N. J. A. Sloane_, Jan 22 2020
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