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Search: id:A000064
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| A000064 |
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Partial sums of (unordered) ways of making change for n cents using coins of 1, 2, 5, 10 cents.
(Formerly M1002 N0375)
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+0
1
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| 1, 2, 4, 6, 9, 13, 18, 24, 31, 39, 50, 62, 77, 93, 112, 134, 159, 187, 218, 252, 292, 335, 384, 436, 494, 558, 628, 704, 786, 874, 972, 1076, 1190, 1310, 1440, 1580, 1730, 1890, 2060, 2240, 2435, 2640, 2860, 3090, 3335, 3595, 3870, 4160, 4465, 4785, 5126
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 152.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Christian G. Bower, Table of n, a(n) for n=0..1000
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FORMULA
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G.f.: 1 / ( 1 - x )^2 ( 1 - x^2 ) ( 1 - x^5 ) ( 1 - x^10 ).
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MAPLE
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1/(1-x)^2/(1-x^2)/(1-x^5)/(1-x^10)
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]
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PROGRAM
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(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))
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CROSSREFS
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Cf. A000008.
Sequence in context: A079717 A114830 A001304 this_sequence A001305 A088575 A026906
Adjacent sequences: A000061 A000062 A000063 this_sequence A000065 A000066 A000067
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Corrected and extended by Simon Plouffe (simon.plouffe(AT)gmail.com)
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