A258800 The number of zeroless decimal numbers whose digital sum is n.
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
Offset: 0
Examples
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.
Crossrefs
Programs
-
Mathematica
CoefficientList[ Series[-1 + 1/(1 - x (1 + x + x^2) (1 + x^3 + x^6)), {x, 0, 36}], x]
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)).
Comments