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

0,3

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

Table of n, a(n) for n=0..36.

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