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A033930 Base 10 digital convolution sequence. 3

%I #18 Feb 12 2017 16:47:21

%S 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,

%T 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,

%U 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

%N Base 10 digital convolution sequence.

%C Differs from A007953 at n=0, 101-109, 111-119 etc. [_R. J. Mathar_, Oct 20 2008]

%H Indranil Ghosh, <a href="/A033930/b033930.txt">Table of n, a(n) for n = 0..10000</a>

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

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

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

%K nonn,base

%O 0,3

%A _David W. Wilson_

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