

A179819


Monetary amounts in U.S. cents such that the smallest number of coins summing to the amount uses only denominations of 10 cents and above.


0



10, 20, 25, 35, 45, 50, 60, 70, 75, 85, 95, 100, 110, 120, 125, 135, 145, 150, 160, 170, 175, 185, 195, 200, 210, 220, 225, 235, 245, 250, 260, 270, 275, 285, 295, 300, 310, 320, 325, 335, 345, 350, 360, 370, 375, 385, 395, 400, 410, 420, 425, 435, 445, 450, 460, 470, 475, 485, 495, 500, 510, 520, 525, 535, 545, 550, 560
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OFFSET

1,1


COMMENTS

U.S. coins are the cent ("penny") (1 cent), nickel (5 cents), dime (10 cents), quarter dollar ("quarter") (25 cents), half dollar (50 cents), and dollar (100 cents).
For values above 100, one can simply add 100 to the previous terms: a(n) = a(n12) + 100.  R. J. Mathar, Aug 05 2010


LINKS



FORMULA

a(n) = +a(n1) +a(n3) a(n4).
G.f.: 5*x*(2+2*x+x^2) / ( (1+x+x^2)*(x1)^2 ). (End)


EXAMPLE

A total amount of 30 cents can be obtained using 3 coins as 10+10+10, but the only way to obtain 30 cents using 2 coins (which is the minimum number of coins) is as 25+5 (which includes a coin smaller than a 10cent piece), so 30 is not in the sequence.
Shortest partitions of multiples of 5 into parts of 5, 10, 25, 50, 100:
5 = 5
10 = 10 a(1)
15 = 5 + 10
20 = 10 + 10 a(2)
25 = 25 a(3)
30 = 5 + 25
35 = 10 + 25 a(4)
40 = 5 + 10 + 25
45 = 10 + 10 + 25 a(5)
50 = 50 a(6)
55 = 5 + 50
60 = 10 + 50 a(7)
65 = 5 + 10 + 50
70 = 10 + 10 + 50 a(8)
75 = 25 + 50 a(9)
80 = 5 + 25 + 50
85 = 10 + 25 + 50 a(10)
90 = 5 + 10 + 25 + 50
95 = 10 + 10 + 25 + 50 a(11)
100 = 100. a(12)
(End)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



