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%I #17 Apr 05 2017 05:39:49
%S 1,1,2,3,5,9,15,26,44,75,129,220,377,644,1101,1883,3219,5505,9412,
%T 16093,27517,47049,80448,137553,235195,402148,687611,1175712,2010288,
%U 3437288,5877241,10049189,17182590,29379620,50234693,85893702
%N Number of ways of making change for n cents using coins of sizes 1, 2, 5, 10 cents, when order matters.
%D Peter Boros (borospet(AT)freemail.hu): Lectures on Fibonacci's World at the SOTERIA Foundation, 1999.
%D P. Henrici, Applied and Computational Complex Analysis. Wiley, NY, 3 vols., 1974-1986. (Vol. 1, p. 580.)
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,1,0,0,0,0,1).
%F a(n) = a(n-1) + a(n-2) + a(n-5) + a(n-10), a(0)=1.
%F G.f.: 1/(1 - x - x^2 - x^5 - x^10). - _Franklin T. Adams-Watters_, Oct 24 2006
%F With offset 1, the INVERT transform of (1 + x + x^4 + x^9). - _Gary W. Adamson_, Apr 04 2017
%e 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.
%p 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
%Y Cf. A079971.
%K easy,nonn
%O 0,3
%A _Miklos Kristof_, Aug 22 2002
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