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Search: id:A073031
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| A073031 |
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Number of ways of making change for n cents using coins of sizes 1, 2, 5, 10 cents, when order matters. |
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+0
5
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| 1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 129, 220, 377, 644, 1101, 1883, 3219, 5505, 9412, 16093, 27517, 47049, 80448, 137553, 235195, 402148, 687611, 1175712, 2010288, 3437288, 5877241, 10049189, 17182590, 29379620, 50234693, 85893702
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Peter Boros (borospet(AT)freemail.hu): Lectures on Fibonacci's World at the SOTERIA Foundation, 1999.
P. Henrici, Applied and Computational Complex Analysis. Wiley, NY, 3 vols., 1974-1986. (Vol. 1, p. 580.)
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FORMULA
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a(n)=a(n-1)+a(n-2)+a(n-5)+a(n-10), a(0)=1.
G.f. 1/(1-x-x^2-x^5-x^10). - Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 24 2006
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EXAMPLE
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a(4)=5 because 4=1+1+1+1=1+1+2=1+2+1=2+1+1=2+2: five possible exchange. a(15)=a(14)+a(13)+a(10)+a(5)=1883=1101+644+129+9.
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MAPLE
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a:= n-> (Matrix(10, (i, j)-> if i+1=j or j=1 and member (i , [1, 2, 5, 10]) then 1 else 0 fi)^n)[1, 1]: seq (a(n), n=0..35); [From Alois P. Heinz (heinz(AT)hs-heilbronn.de), Oct 07 2008]
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CROSSREFS
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Cf. A079971.
Adjacent sequences: A073028 A073029 A073030 this_sequence A073032 A073033 A073034
Sequence in context: A034073 A114623 A079971 this_sequence A114138 A114140 A096816
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KEYWORD
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easy,nonn
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AUTHOR
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Miklos Kristof (kristmikl(AT)freemail.hu), Aug 22 2002
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