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

Author

David W. Wilson

Keywords

• nonn
• base

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

Programs

Mathematica

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

PARI

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

Formula

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