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A001362 Number of ways of making change for n cents using coins of 1, 2, 4, 10 cents.

%I A001362 #35 Feb 01 2022 01:33:13
%S A001362 1,1,2,2,4,4,6,6,9,9,13,13,18,18,24,24,31,31,39,39,49,49,60,60,73,73,
%T A001362 87,87,103,103,121,121,141,141,163,163,187,187,213,213,242,242,273,
%U A001362 273,307,307,343,343,382,382,424,424,469,469,517,517,568,568,622,622
%N A001362 Number of ways of making change for n cents using coins of 1, 2, 4, 10 cents.
%C A001362 Number of partitions of n into parts 1, 2, 4, and 10. - _Joerg Arndt_, Sep 05 2014
%D A001362 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 316.
%D A001362 G. Pólya and G. Szegő, Problems and Theorems in Analysis, Springer-Verlag, NY, 2 vols., 1972, Vol. 1, p. 1.
%H A001362 T. D. Noe, <a href="/A001362/b001362.txt">Table of n, a(n) for n = 0..1000</a>
%H A001362 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=186">Encyclopedia of Combinatorial Structures 186</a>
%H A001362 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H A001362 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1, 1, -1, -1, 1, 0, 0, 1, -1, -1, 1, -1, 1, 1, -1).
%F A001362 G.f.: 1/((1-x)*(1-x^2)*(1-x^4)*(1-x^10)).
%p A001362 1/(1-x)/(1-x^2)/(1-x^4)/(1-x^10): seq(coeff(series(%,x,n+1),x,n), n=0..80);
%t A001362 nn = 1000; CoefficientList[Series[1/((1 - x^1) (1 - x^2) (1 - x^4) (1 - x^10)), {x, 0, nn}], x] (* _T. D. Noe_, Jun 28 2012 *)
%t A001362 Table[Length[FrobeniusSolve[{1,2,4,10},n]],{n,0,60}] (* _Harvey P. Dale_, May 20 2021 *)
%o A001362 (PARI) a(n)=floor((n\2+8)*(2*(n\2)^2+11*(n\2)+18)/120) \\ _Tani Akinari_, May 14 2014
%Y A001362 Twice A001304.
%K A001362 nonn
%O A001362 0,3
%A A001362 _N. J. A. Sloane_