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 A119651 Number of different values of exactly n standard American coins (pennies, nickels, dimes and quarters). 1
 4, 10, 20, 34, 52, 73, 96, 120, 144, 168, 192, 216, 240, 264, 288, 312, 336, 360, 384, 408, 432, 456, 480, 504, 528, 552, 576, 600, 624, 648, 672, 696, 720, 744, 768, 792, 816, 840, 864, 888, 912, 936, 960, 984, 1008, 1032, 1056, 1080, 1104, 1128, 1152 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..250 FORMULA Conjectures from Colin Barker, Oct 24 2019: (Start) G.f.: x*(4 + 2*x + 4*x^2 + 4*x^3 + 4*x^4 + 3*x^5 + 2*x^6 + x^7) / (1 - x)^2. a(n) = 2*a(n-1) - a(n-2) for n>2. a(n) = 24*(n-3) for n>6. (End) EXAMPLE If you have 4 types of objects (coin denominations) you can have 35 different sets of 4. Out of these 35 only two have the same value: you can make 40 cents out of 4 dimes or out of a quarter and 3 nickels. Thus a(4) = 34. PROG (PARI) a(n) = {#select(k->k>0, Vec(polcoef(1/(1 - x*(y + y^5 + y^10 + y^25)) + O(x*x^n), n)))} \\ Andrew Howroyd, Oct 24 2019 CROSSREFS Sequence in context: A019457 A099589 A008141 * A279015 A005893 A301034 Adjacent sequences:  A119648 A119649 A119650 * A119652 A119653 A119654 KEYWORD nonn AUTHOR Tanya Khovanova, Jul 28 2006 STATUS approved

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Last modified September 21 11:46 EDT 2020. Contains 337268 sequences. (Running on oeis4.)