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 A000064 Partial sums of (unordered) ways of making change for n cents using coins of 1, 2, 5, 10 cents. (Formerly M1002 N0375) 1
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of partitions of n into two kinds of part 1 and one kind of parts 2, 5, and 10. - Joerg Arndt, May 10 2014 REFERENCES 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). LINKS Christian G. Bower, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1,1,-2,0,2,-1,1,-2,0,2,-1,-1,2,0,-2,1). FORMULA G.f.: 1 / ( ( 1 - x )^2 * ( 1 - x^2 ) * ( 1 - x^5 ) * ( 1 - x^10 ) ). a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) + a(n-5) - 2*a(n-6) + 2*a(n-8) - a(n-9) + a(n-10) - 2*a(n-11) + 2*a(n-13) - a(n-14) - a(n-15) + 2*a(n-16) - 2*a(n-18) + a(n-19). - Fung Lam, May 07 2014 MAPLE 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); # Alois P. Heinz, Oct 05 2008 MATHEMATICA CoefficientList[Series[1/((1-x)^2(1-x^2)(1-x^5)(1-x^10)), {x, 0, 100}], x] (* Vladimir Joseph Stephan Orlovsky, Jan 25 2012 *) PROG (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)) (PARI) a(n)=floor((n^4+38*n^3+476*n^2+2185*n+3735)/2400+(n+1)*(-1)^n/160+(n\5+1)*[0, 0, 1, 0, -1][n%5+1]/10) \\ Tani Akinari, May 10 2014 CROSSREFS Cf. A000008. Sequence in context: A114830 A177239 A001304 * A001305 A088575 A177189 Adjacent sequences:  A000061 A000062 A000063 * A000065 A000066 A000067 KEYWORD nonn,easy AUTHOR EXTENSIONS Corrected and extended by Simon Plouffe STATUS approved

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Last modified September 21 11:18 EDT 2019. Contains 327253 sequences. (Running on oeis4.)