|
%I #30 Nov 10 2018 08:52:26
%S 0,1,2,3,4,1,2,3,4,5,1,2,3,4,5,2,3,4,5,6,2,3,4,5,6,1,2,3,4,5,2,3,4,5,
%T 6,2,3,4,5,6,3,4,5,6,7,3,4,5,6,7,1,2,3,4,5,2,3,4,5,6,2,3,4,5,6,3,4,5,
%U 6,7,3,4,5,6,7,2,3,4,5,6,3,4,5,6,7,3,4,5,6,7,4,5,6,7,8,4,5,6,7,8,2,3
%N Minimal number of coins needed to pay n cents using coins of sizes 1, 5, 10, 25, 50 cents.
%H Alois P. Heinz, <a href="/A011542/b011542.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H <a href="/index/Rec#order_51">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1).
%F G.f.: -(6*x^49 -x^48 -x^47 -x^46 -x^45 +4*x^44 -x^43 -x^42 -x^41 -x^40 +3*x^39 -x^38 -x^37 -x^36 -x^35 +4*x^34 -x^33 -x^32 -x^31 -x^30 +3*x^29 -x^28 -x^27 -x^26 -x^25 +5*x^24 -x^23 -x^22 -x^21 -x^20 +4*x^19 -x^18 -x^17 -x^16 -x^15 +3*x^14 -x^13 -x^12 -x^11 -x^10 +4*x^9 -x^8 -x^7 -x^6 -x^5 +3*x^4 -x^3 -x^2 -x -1)*x / (x^51-x^50-x+1). - _Alois P. Heinz_, Aug 04 2014
%t f[n_]:=Total[Quotient[Most[FoldList[Mod,n,{50,25,10,5,1}]],{50,25,10,5,1}]];Table[f[n],{n,1,84}] (* _Geoffrey Critzer_, May 04 2013 *)
%t Table[Min[Total/@FrobeniusSolve[{1,5,10,25,50},n]],{n,0,110}] (* _Harvey P. Dale_, Nov 10 2018 *)
%Y Cf. A053344.
%K nonn,easy
%O 0,3
%A Frank J. Stadermann (df6s(AT)HRZPUB.th-darmstadt.de)
|
