OFFSET
0,6
COMMENTS
Sequence definition and Scratch program to compute the 100 terms due to Skylar Sutherland. Generating function contributed by Andrew V. Sutherland. Related to A001299, but distinguishes permutations of coin types.
REFERENCES
Skylar Sutherland, student presentation at "The Undiscovered Country", a course for young mathematicians. Part of MIT's Educational Studies Program.
FORMULA
Let A_v(x,y) = 1-y+y/(1-x)^v and A(x,y) = A_1(x,y)A_5(x,y)A_10(x,y)A_25(x,y). Let A^(k)(x,y) denote the k-th partial derivative of A(x,y) w.r.t. y. The generating function of a(n) is A(x) = Sum A^(k)(x,0) for k from 0 to 4.
EXAMPLE
a(16) = 15 = 1+2*4+6*1 since the distinct Skylar stackings of 16 cents are:
16p, 11p1n, 1n11p, 6p2n, 2n6p, 1p3n, 3n1p, 1p1d, 1d1p, 1p1n1d, 1p1d1n, 1n1p1d, 1n1d1p, 1d1p1n, 1d1n1p
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew V. Sutherland, Aug 20 2007
STATUS
approved