

A119651


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


1



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
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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(n1)  a(n2) for n>2.
a(n) = 24*(n3) 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: A019457 A099589 A008141 * A279015 A005893 A301034
Adjacent sequences: A119648 A119649 A119650 * A119652 A119653 A119654


KEYWORD

nonn


AUTHOR

Tanya Khovanova, Jul 28 2006


STATUS

approved



