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A129263
Skylar (age 7) counts change by stacking all coins of the same type then arranging the stacks in a row. a(n) is the number of distinct Skylar stackings of n cents using any combination of pennies, nickels, dimes or quarters.
0
1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 5, 7, 7, 7, 7, 10, 15, 15, 15, 15, 19, 25, 25, 25, 25, 31, 41, 41, 41, 41, 49, 63, 63, 63, 63, 74, 95, 95, 95, 95, 111, 147, 147, 147, 147, 166, 209, 209, 209, 209, 234, 293, 293, 293, 293, 322, 391, 391, 391, 391, 427, 515, 515, 515, 515
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
Cf. A001299.
Sequence in context: A369451 A029088 A253591 * A035367 A042959 A147815
KEYWORD
nonn
AUTHOR
STATUS
approved