Search: id:A001301
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%I A001301
%S A001301 1,1,2,2,3,4,5,6,7,8,11,12,15,16,19,22,25,28,31,34,40,43,
%T A001301 49,52,58,65,71,78,84,91,102,109,120,127,138,151,162,175,
%U A001301 186,199,217,230,248,261,279,300,318,339,357,378,406,427
%N A001301 Number of ways of making change for n cents using coins of 1, 2, 5, 10, 
               25 cents.
%D A001301 R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, 
               Reading, MA, 1990, p. 316.
%D A001301 G. P\'{o}lya and G. Szeg\"{o}, Problems and Theorems in Analysis, Springer-Verlag, 
               NY, 2 vols., 1972, Vol. 1, p. 1.
%H A001301 H. Bottomley, <a href="a8.gif">Initial terms of A000008, A001301, A001302, 
               A001312, A001313</a>
%H A001301 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=177">
               Encyclopedia of Combinatorial Structures 177</a>
%H A001301 <a href="Sindx_Mag.html#change">Index entries for sequences related to 
               making change.</a>
%p A001301 1/((1-x)*(1-x^2)*(1-x^5)*(1-x^10)*(1-x^25));
%p A001301 M := Matrix(43, (i,j)-> if (i=j-1) or (j=1 and member(i, [1, 2, 5, 8, 
               10, 13, 16, 17, 25, 28, 31, 32, 36, 37, 40, 43])) then 1 elif j=1 
               and member(i, [3, 6, 7, 11, 12, 15, 18, 26, 27, 30, 33, 35, 38, 41, 
               42]) then -1 else 0 fi); a := n -> (M^(n))[1,1]; seq (a(n), n=0..51); 
               - Alois P. Heinz (heinz(AT)hs-heilbronn.de), Jul 25 2008
%t A001301 CoefficientList[ Series[ 1 / ((1 - x)(1 - x^2)(1 - x^5)(1 - x^10)(1 - 
               x^25)), {x, 0, 55} ], x ]
%Y A001301 Sequence in context: A029015 A000008 A001312 this_sequence A001302 A001313 
               A057537
%Y A001301 Adjacent sequences: A001298 A001299 A001300 this_sequence A001302 A001303 
               A001304
%K A001301 nonn
%O A001301 1,3
%A A001301 N. J. A. Sloane (njas(AT)research.att.com).

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