A033639 Base-2 digital convolution sequence.

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, 297, 376, 1156, 763, 1564, 2592, 6451, 376, 1532, 1139, 4235, 4124, 11714, 8735, 26105, 5263, 21212, 18122, 77153, 35210, 100649, 135748, 369972, 95275, 207638

Offset

0,4

Links

Rémy Sigrist, Table of n, a(n) for n = 0..5000

Rémy Sigrist, PARI program for A033639.

Example

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.

Maple

a:= proc(n) option remember; `if`(n=0, 1, (l->
      add(l[i]*a(n-i), i=1..nops(l)))(Bits[Split](n)))
    end:
seq(a(n), n=0..49);  # Alois P. Heinz, Apr 14 2021

Mathematica

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 *)

Prog

(PARI) See Links section.

Crossrefs

Cf. A033640, A033641, A033642, A033643, A033644, A033645, A033646, A033647, A033666, A033922, A260956.

Sequence in context: A106524 A323641 A086582 * A156565 A156693 A156564

Adjacent sequences: A033636 A033637 A033638 * A033640 A033641 A033642

Keyword

base,nonn

Author

David W. Wilson

Status

approved