A033930 Base 10 digital convolution sequence.

1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 8, 9, 10, 11, 12, 13, 14

Offset

0,3

Comments

Differs from A007953 at n=0, 101-109, 111-119 etc. [R. J. Mathar, Oct 20 2008]

Links

Indranil Ghosh, Table of n, a(n) for n = 0..10000

Formula

For example, a(837) = 8*a(2)+3*a(1)+7*a(0).

Mathematica

a = {1}; Do[AppendTo[a, ListConvolve[Reverse@ Take[a, Length@ #], #][[1]] &@ IntegerDigits@ n], {n, 10^3}]; a (* Michael De Vlieger, Feb 12 2017 *)

Prog

(PARI) a(n) = if (!n, 1, my(d = digits(n)); sum(i=1, #d, d[i]*a(#d-i))); \\ Michel Marcus, Sep 13 2014

Crossrefs

Sequence in context: A177274 A349251 A131650 * A076314 A007953 A080463

Adjacent sequences: A033927 A033928 A033929 * A033931 A033932 A033933

Keyword

nonn,base

Author

David W. Wilson

Status

approved