A033640 Base 3 digital convolution sequence.

1, 1, 2, 1, 3, 7, 6, 20, 52, 6, 26, 104, 32, 162, 460, 356, 1438, 4048, 712, 3588, 15272, 5012, 27460, 90476, 64944, 300816, 912472, 90476, 155420, 611656, 1067892, 1770024, 4763360, 4151704, 14746316, 39566064, 8915064, 27813084, 109938548, 76294212, 222960908

Offset: 0

Author

David W. Wilson

Keywords

• base
• nonn

Examples

			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.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..2000

Crossrefs

Cf. A033639, A033641, A033642, A033643, A033644, A033645, A033646, A033647.

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, (l->
      add(l[i]*a(n-i), i=1..nops(l)))(convert(n, base, 3)))
    end:
seq(a(n), n=0..40);  # Alois P. Heinz, Apr 14 2021