%I #14 May 17 2017 17:59:41
%S 1,1,1,1,2,3,3,4,5,6,7,8,10,11,13,15,17,19,21,24,27,30,33,36,40,44,48,
%T 52,57,62,67,72,78,84,90,97,104,111,118,126,135,143,152,161,171,181,
%U 191,202,213,225,237,249,262
%N Expansion of 1/((1-x)*(1-x^4)*(1-x^5)*(1-x^7)).
%C Number of partitions of n into parts 1, 4, 5 and 7. - _Ilya Gutkovskiy_, May 17 2017
%H G. C. Greubel, <a href="/A029064/b029064.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,1,0,-1,1,-1,-1,1,-1,0,1,0, 0,1,-1).
%F a(n) = floor((2*n^3+51*n^2+388*n+1680)/1680). - _Tani Akinari_, May 23 2014
%F a(-17 - n) = -a(n). - _Michael Somos_, May 23 2014
%e G.f. = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + 6*x^9 + ...
%t a[ n_] := Quotient[ 2 n^3 + 51 n^2 + 388 n, 1680] + 1; (* _Michael Somos_, May 23 2014 *)
%t CoefficientList[Series[1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^7)), {x, 0, 50}], x] (* _G. C. Greubel_, May 17 2017 *)
%o (PARI) {a(n) = (2*n^3 + 51*n^2 + 388*n) \ 1680 + 1}; /* _Michael Somos_, May 23 2014 */
%o (PARI) x='x+O('x^50); Vec(1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^7))) \\ _G. C. Greubel_, May 17 2017
%K nonn
%O 0,5
%A _N. J. A. Sloane_, Dec 11 1999
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