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 A338551 Number of ways to make a checkout score of n in darts. 1
 0, 1, 1, 4, 7, 14, 20, 31, 39, 55, 65, 86, 96, 126, 133, 171, 179, 223, 228, 286, 283, 352, 348, 422, 408, 497, 467, 569, 534, 642, 594, 720, 654, 791, 719, 863, 775, 942, 831, 1012, 894, 1082, 945, 1159, 991, 1216, 1037, 1263, 1062, 1311, 1081, 1340, 1110, 1366 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS In other words, the number of ways to achieve a score of n using at most 3 darts and finishing on a double. The maximum checkout score is 170, so this is a finite sequence. LINKS Carmen Bruni, Table of n, a(n) for n = 1..170 Wikipedia, Darts PROG (Python) def darts(n): if n > 170 or n <= 1: return 0 ans = 0 singles = list(range(1, 21)) + [25] doubles = list(map(lambda x: 2*x, singles)) triples = list(map(lambda x: 3*x, singles[:-1])) throws = singles+doubles+triples for i in range(len(throws)): for j in range(len(throws)): for k in range(len(doubles)): dart1 = throws[i] dart2 = throws[j] dart3 = doubles[k] if dart1 + dart2 + dart3 == n: ans += 1 for j in range(len(doubles)): dart1 = throws[i] dart2 = doubles[j] if dart1 + dart2 == n: ans += 1 return ans + (n in doubles) for i in range(1, 171): print(darts(i)) (PARI) seq()={my(s=x*(1-x^20)/(1-x)+x^25, d=subst(s, x, x^2), g=s+d+subst(s-x^25, x, x^3)); Vecrev((1+g+g^2)*d/x)} \\ Andrew Howroyd, Nov 04 2020 CROSSREFS Cf. A008575, A242718, A242678, A242681, A167213, A076119, A244512, A117883. Sequence in context: A161426 A115759 A157615 * A188319 A171378 A147478 Adjacent sequences: A338548 A338549 A338550 * A338552 A338553 A338554 KEYWORD nonn,fini,full AUTHOR Carmen Bruni, Nov 02 2020 STATUS approved

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Last modified December 2 19:59 EST 2022. Contains 358510 sequences. (Running on oeis4.)