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 A258800 The number of zeroless decimal numbers whose digital sum is n. 1
 0, 1, 2, 4, 8, 16, 32, 64, 128, 256, 511, 1021, 2040, 4076, 8144, 16272, 32512, 64960, 129792, 259328, 518145, 1035269, 2068498, 4132920, 8257696, 16499120, 32965728, 65866496, 131603200, 262947072, 525375999, 1049716729, 2097364960, 4190597000, 8372936304, 16729373488, 33425781248 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS If you were to include decimal numbers that contain any number of zeros, then a(n) would be infinity. If on the other hand, you limit the number of zeros to some number, then a(n) is finite. LINKS FORMULA a(n) = A104144(n+8) for n>0. G.f.: -(x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9)/(-1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9) = -1 + 1/(1-x(1 + x + x^2)(1 + x^3 + x^6)). EXAMPLE a(0) = 0 since there exists no decimal number lacking a zero whose digital sum is zero. a(1) = 1 since there exists only one zeroless decimal number whose digital sum is one and that number is 1. a(2) = 2 since there exist only two zeroless decimal numbers whose digital sum is two and they are 2 & 11. a(3) = 4 since there exist only four zeroless decimal numbers whose digital sum is three and they are 3, 21, 12 & 111. a(4) = 8 since there exist only eight zeroless decimal numbers whose digital sum is four and they are 4, 31, 13, 22, 211, 121, 112 & 1111. MATHEMATICA CoefficientList[ Series[-1 + 1/(1 - x (1 + x + x^2) (1 + x^3 + x^6)), {x, 0, 36}], x] CROSSREFS Cf. A104144. Cf. A125630, A125858, A125858, A125880, A125897, A125904, A125908, A125909, A125910, A125945, A125946, A125947, A125948, A126627, A126628, A126629, A126631, A126632, A126633, A126634, A126635, A126639, A126640, A126641, A126642, A126643, A126644, A126645, A126646, A126718. Cf. A211072. Sequence in context: A172318 A234590 A104144 * A194632 A282584 A251759 Adjacent sequences:  A258797 A258798 A258799 * A258801 A258802 A258803 KEYWORD nonn,base AUTHOR Robert G. Wilson v, Jun 10 2015 STATUS approved

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Last modified August 16 11:28 EDT 2022. Contains 356168 sequences. (Running on oeis4.)