A119651 Number of different values of exactly n standard American coins (pennies, nickels, dimes and quarters).

4, 10, 20, 34, 52, 73, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, 576, 600, 624, 648, 672, 696, 720, 744, 768, 792, 816, 840, 864, 888, 912, 936, 960, 984, 1008, 1032, 1056, 1080, 1104, 1128, 1152

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..250

Formula

Conjectures from Colin Barker, Oct 24 2019: (Start)

G.f.: x*(4 + 2*x + 4*x^2 + 4*x^3 + 4*x^4 + 3*x^5 + 2*x^6 + x^7) / (1 - x)^2.

a(n) = 2*a(n-1) - a(n-2) for n>2.

a(n) = 24*(n-3) for n>6.

(End)

Example

If you have 4 types of objects (coin denominations) you can have 35 different sets of 4. Out of these 35 only two have the same value: you can make 40 cents out of 4 dimes or out of a quarter and 3 nickels. Thus a(4) = 34.

Prog

(PARI) a(n) = {#select(k->k>0, Vec(polcoef(1/(1 - x*(y + y^5 + y^10 + y^25)) + O(x*x^n), n)))} \\ Andrew Howroyd, Oct 24 2019

Crossrefs

Sequence in context: A360050 A099589 A008141 * A279015 A005893 A301034

Adjacent sequences: A119648 A119649 A119650 * A119652 A119653 A119654

Keyword

nonn

Author

Tanya Khovanova, Jul 28 2006

Status

approved