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(n-12) + 100. - R. J. Mathar, Aug 05 2010
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
From R. J. Mathar, Aug 05 2010: (Start)
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)
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 10-cent piece), so 30 is not in the sequence.
From R. J. Mathar, Aug 05 2010: (Start)
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
J. Lowell, Jul 28 2010
EXTENSIONS
More terms from R. J. Mathar, Aug 05 2010
More terms from Max Alekseyev, Oct 15 2012
STATUS
approved