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A011542
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Minimal number of coins needed to pay n cents using coins of sizes 1, 5, 10, 25, 50 cents.
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5
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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, 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, 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
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OFFSET
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0,3
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LINKS
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Index entries for linear recurrences with constant coefficients, 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).
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FORMULA
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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
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MATHEMATICA
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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 *)
Table[Min[Total/@FrobeniusSolve[{1, 5, 10, 25, 50}, n]], {n, 0, 110}] (* Harvey P. Dale, Nov 10 2018 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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Frank J. Stadermann (df6s(AT)HRZPUB.th-darmstadt.de)
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STATUS
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approved
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