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%I #28 Jul 25 2023 04:03:59
%S 1,1,1,2,1,2,3,6,1,3,4,13,4,11,21,49,13,17,24,62,66,103,145,338,128,
%T 297,376,1156,763,1564,2592,6451,376,1532,1139,4235,4124,11714,8735,
%U 26105,5263,21212,18122,77153,35210,100649,135748,369972,95275,207638
%N Base-2 digital convolution sequence.
%H Rémy Sigrist, <a href="/A033639/b033639.txt">Table of n, a(n) for n = 0..5000</a>
%H Rémy Sigrist, <a href="/A033639/a033639.gp.txt">PARI program for A033639</a>.
%e Suppose base = 3 and a(0)..a(13) are 1, 1, 2, 1, 3, 7, 6, 20, 52, 6, 26, 104, 32, 162. In base 3, 14 = 112, so we convolve the last three terms with 1, 1, 2 to obtain 104*1 + 32*1 + 162*2 = 460.
%p a:= proc(n) option remember; `if`(n=0, 1, (l->
%p add(l[i]*a(n-i), i=1..nops(l)))(Bits[Split](n)))
%p end:
%p seq(a(n), n=0..49); # _Alois P. Heinz_, Apr 14 2021
%t a[0] = 1; a[n_] := a[n] = Total[(d = IntegerDigits[n, 2]) * Table[a[n - Length[d] + k - 1], {k, 1, Length[d]}]]; Array[a, 50, 0] (* _Amiram Eldar_, Jul 25 2023 *)
%o (PARI) See Links section.
%Y Cf. A033640, A033641, A033642, A033643, A033644, A033645, A033646, A033647, A033666, A033922, A260956.
%K base,nonn
%O 0,4
%A _David W. Wilson_
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