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A073031 Number of ways of making change for n cents using coins of sizes 1, 2, 5, 10 cents, when order matters. 5
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; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

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.)

LINKS

Table of n, a(n) for n=0..35.

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,1,0,0,0,0,1).

FORMULA

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, Oct 24 2006

With offset 1, the INVERT transform of (1 + x + x^4 + x^9). - Gary W. Adamson, Apr 04 2017

EXAMPLE

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.

MAPLE

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); # Alois P. Heinz, Oct 07 2008

CROSSREFS

Cf. A079971.

Sequence in context: A034073 A114623 A079971 * A114138 A114140 A302018

Adjacent sequences:  A073028 A073029 A073030 * A073032 A073033 A073034

KEYWORD

easy,nonn

AUTHOR

Miklos Kristof, Aug 22 2002

STATUS

approved

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Last modified September 28 16:11 EDT 2021. Contains 347716 sequences. (Running on oeis4.)