

A119652


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


0



4, 13, 27, 46, 69, 94, 119, 144, 169, 194, 219, 244, 269, 294, 319, 344, 369, 394, 419, 444, 469, 494, 519, 544, 569, 594, 619, 644, 669, 694, 719, 744, 769, 794, 819, 844, 869, 894, 919, 944, 969, 994, 1019, 1044, 1069, 1094, 1119, 1144, 1169, 1194, 1219
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..51.


FORMULA

Conjectures from Colin Barker, Oct 25 2019: (Start)
G.f.: x*(4 + 5*x + 5*x^2 + 5*x^3 + 4*x^4 + 2*x^5) / (1  x)^2.
a(n) = 2*a(n1)  a(n2) for n>6.
a(n) = 25*n56 for n>4.
(End)


EXAMPLE

If you have 1 coin you can have 4 different totals: 1, 5, 10 and 25. If you have 2 coins, you can have 10 totals: 2, 6, 10, 11, 15, 20, 26, 30, 35, 50. Notice that the same total appears twice: 10 is one dime and two nickels. Hence a(2) = 13.


MATHEMATICA

Join[{4, 13, 27, 46}, Range[69, 2000, 25]] (* Vladimir Joseph Stephan Orlovsky, Jun 15 2011 *)


CROSSREFS

Cf. A008607.
Sequence in context: A305356 A304946 A316616 * A147875 A321988 A108753
Adjacent sequences: A119649 A119650 A119651 * A119653 A119654 A119655


KEYWORD

nonn,changed


AUTHOR

Tanya Khovanova, Jul 28 2006


STATUS

approved



