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%I #18 Sep 08 2022 08:44:50
%S 1,1,2,2,3,4,5,7,8,10,12,14,17,19,23,26,30,34,38,43,48,54,60,66,73,80,
%T 88,96,105,114,124,134,145,156,168,181,194,208,222,237,253,269,287,
%U 304,323,342,362,383,404,427,450
%N Expansion of 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)).
%C Number of partitions of n into parts 1, 2, 5, and 7. - _Joerg Arndt_, Oct 15 2014
%H <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1,0,1,-1,0,0,-1,1,0,-1,1,1,-1).
%F G.f.: 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)).
%F a(n) = floor((2*n^3+45*n^2+298*n+956)/840+(-1)^n/16). - _Tani Akinari_, Oct 15 2014
%t CoefficientList[Series[1/((1 - x) (1 - x^2) (1 - x^5) (1 - x^7)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Oct 15 2014 *)
%o (Magma) [Floor((2*n^3+45*n^2+298*n+956)/840+(-1)^n/16): n in [0..60]]; // _Vincenzo Librandi_, Oct 15 2014
%o (PARI) Vec(1/((1-x)*(1-x^2)*(1-x^5)*(1-x^7)) + O(x^80)) \\ _Michel Marcus_, Oct 15 2014
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_
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