A119652 Number of different values of <= n standard American coins (pennies, nickels, dimes and quarters).

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

Offset: 1

Author

Tanya Khovanova, Jul 28 2006

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A008607.

Programs

Mathematica

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

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(n-1) - a(n-2) for n>6.

a(n) = 25*n-56 for n>4.

(End)