A245573 - OEIS

%I #25 Feb 27 2017 03:31:21

%S 0,1,1,2,2,1,2,2,3,3,1,2,2,3,3,2,3,3,4,4,2,3,3,4,4,3,4,4,5,5,3,4,4,5,

%T 5,4,5,5,6,6,4,5,5,6,6,5,6,6,7,7,5,6,6,7,7,6,7,7,8,8,6,7,7,8,8,7,8,8,

%U 9,9,7,8,8,9,9,8,9,9,10,10,8,9,9,10,10,9,10,10,11,11,9,10,10,11,11,10,11,11,12,12,10,11,11,12

%N Minimal coin changing sequence for denominations 1, 2, 5 and 10 cents.

%H Colin Barker, <a href="/A245573/b245573.txt">Table of n, a(n) for n = 0..1000</a>

%H Bailor Tow, <a href="http://math.stackexchange.com/questions/260404/finding-recurrence-and-an-algorithm-to-represent-it">Coin changing problem</a>,  Maths StackExchange

%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,0,0,0,0,1,-1).

%F From _Colin Barker_, Feb 22 2017: (Start)

%F a(n) = a(n-1) + a(n-10) - a(n-11) for n>10.

%F G.f.: x*(1 + x^2 - x^4 + x^5 + x^7 - 2*x^9) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)).

%F (End)

%t CoefficientList[Series[x (1 + x^2 - x^4 + x^5 + x^7 - 2 x^9)/((1 - x)^2*(1 + x) (1 - x + x^2 - x^3 + x^4) (1 + x + x^2 + x^3 + x^4)), {x, 0, 103}], x] (* _Michael De Vlieger_, Feb 22 2017 *)

%o (PARI) concat(0, Vec(x*(1 + x^2 - x^4 + x^5 + x^7 - 2*x^9) / ((1 - x)^2*(1 + x)*(1 - x + x^2 - x^3 + x^4)*(1 + x + x^2 + x^3 + x^4)) + O(x^100))) \\ _Colin Barker_, Feb 22 2017

%K nonn,easy

%O 0,4

%A _Marko Riedel_, Jul 25 2014

%E a(0)=0 prepended by _Alois P. Heinz_, May 26 2015