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%I A011542 #30 Nov 10 2018 08:52:26
%S A011542 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 A011542 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 A011542 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 A011542 Minimal number of coins needed to pay n cents using coins of sizes 1, 5, 10, 25, 50 cents.
%H A011542 Alois P. Heinz, <a href="/A011542/b011542.txt">Table of n, a(n) for n = 0..1000</a>
%H A011542 <a href="/index/Mag#change">Index entries for sequences related to making change.</a>
%H A011542 <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 A011542 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 A011542 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 A011542 Table[Min[Total/@FrobeniusSolve[{1,5,10,25,50},n]],{n,0,110}] (* _Harvey P. Dale_, Nov 10 2018 *)
%Y A011542 Cf. A053344.
%K A011542 nonn,easy
%O A011542 0,3
%A A011542 Frank J. Stadermann (df6s(AT)HRZPUB.th-darmstadt.de)

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