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

0,3

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).

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

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 *)

Crossrefs

Cf. A053344.

Sequence in context: A159957 A053840 A010883 * A260688 A053344 A092196

Adjacent sequences: A011539 A011540 A011541 * A011543 A011544 A011545

Keyword

nonn,easy

Author

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

Status

approved