A011542 Minimal number of coins needed to pay n cents using coins of sizes 1, 5, 10, 25, 50 cents.

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

Offset: 0

Author

Frank J. Stadermann (df6s(AT)HRZPUB.th-darmstadt.de)

Keywords

• nonn
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• Index entries for sequences related to making change.
• 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).

Crossrefs

Cf. A053344.

Programs

Mathematica

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 *)

Formula

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