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A114140
Number of ordered sequences of coins (each of which has value 1, 2, 5, 10 or 20) which add to n.
3
1, 1, 2, 3, 5, 9, 15, 26, 44, 75, 129, 220, 377, 644, 1101, 1883, 3219, 5505, 9412, 16093, 27518, 47051, 80453, 137563, 235215, 402188, 687688, 1175860, 2010567, 3437810, 5878212, 10050981, 17185883, 29385638, 50245647, 85913568, 146901103, 251181919
OFFSET
0,3
COMMENTS
Equivalently, number of sequences of coins (each of which has value 5, 10, 25, 50 or 100) which add to 5n.
Based on "silver" US coins as of Feb 22 2006.
Number of compositions of n into parts 1, 2, 5, 10, and 20. - Joerg Arndt, Sep 19 2014
FORMULA
G.f.: 1/(1-(x+x^2+x^5+x^10+x^20)).
MAPLE
A114140 := proc(n)
coeftayl( 1/(1-(x+x^2+x^5+x^10+x^20)), x=0, n);
end proc:
seq(A114140(n), n=0..30); # Wesley Ivan Hurt, Sep 18 2014
MATHEMATICA
CoefficientList[Series[1/(1 - (x + x^2 + x^5 + x^10 + x^20)), {x, 0, 30}], x] (* Wesley Ivan Hurt, Sep 18 2014 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved