Search: id:A000064
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%I A000064 M1002 N0375
%S A000064 1,2,4,6,9,13,18,24,31,39,50,62,77,93,112,134,159,187,218,252,292,335,
%T A000064 384,436,494,558,628,704,786,874,972,1076,1190,1310,1440,1580,1730,
%U A000064 1890,2060,2240,2435,2640,2860,3090,3335,3595,3870,4160,4465,4785,5126
%N A000064 Partial sums of (unordered) ways of making change for n cents using coins 
               of 1, 2, 5, 10 cents.
%D A000064 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A000064 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A000064 J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 
               152.
%H A000064 Christian G. Bower, <a href="b000064.txt">Table of n, a(n) for n=0..1000</
               a>
%F A000064 G.f.: 1 / ( 1 - x )^2 ( 1 - x^2 ) ( 1 - x^5 ) ( 1 - x^10 ).
%p A000064 1/(1-x)^2/(1-x^2)/(1-x^5)/(1-x^10)
%p A000064 a:= proc(n) local m, r; m := iquo (n, 10, 'r'); r:= r+1; (55+ (119+ (95+ 
               25*m) *m) *m) *m/6+ [1, 2, 4, 6, 9, 13, 18, 24, 31, 39][r]+ [0, 26, 
               61, 99, 146, 202, 267, 341, 424, 516][r]*m/6+ [0, 10, 21, 33, 46, 
               60, 75, 91, 108, 126][r]*m^2/2+ (5*r-5) *m^3/3 end: seq (a(n), n=0..100); 
               [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 05 2008]
%o A000064 (PARI) a(n)=if(n<0,0,polcoeff(1/((1-x)^2*(1-x^2)*(1-x^5)*(1-x^10))+x*O(x^n),
               n))
%Y A000064 Cf. A000008.
%Y A000064 Sequence in context: A079717 A114830 A001304 this_sequence A001305 A088575 
               A026906
%Y A000064 Adjacent sequences: A000061 A000062 A000063 this_sequence A000065 A000066 
               A000067
%K A000064 nonn,easy
%O A000064 0,2
%A A000064 N. J. A. Sloane (njas(AT)research.att.com).
%E A000064 Corrected and extended by Simon Plouffe (simon.plouffe(AT)gmail.com)

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