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A179819
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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.
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0
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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
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1,1
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COMMENTS
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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(n-12) + 100. - R. J. Mathar, Aug 05 2010
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LINKS
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FORMULA
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a(n) = +a(n-1) +a(n-3) -a(n-4).
G.f.: 5*x*(2+2*x+x^2) / ( (1+x+x^2)*(x-1)^2 ). (End)
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EXAMPLE
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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 10-cent 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)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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