A316080 Sequence shifts left eight places under Weigh transform with a(n) = signum(n) for n<8.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 13, 17, 22, 30, 40, 53, 71, 96, 128, 173, 233, 314, 425, 575, 780, 1060, 1442, 1964, 2680, 3658, 5000, 6840, 9366, 12835, 17604, 24164, 33194, 45632, 62775, 86417, 119038, 164077, 226287, 312261, 431138

Offset

0,12

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2500

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 * Product_{n>=1} (1 + x^n)^a(n). - Ilya Gutkovskiy, May 09 2019

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(binomial(a(i), j)*b(n-i*j, i-1), j=0..n/i)))
    end:
a:= n-> (k-> `if`(n<k, signum(n), b(n-k$2)))(8):
seq(a(n), n=0..53);

Crossrefs

Column k=8 of A316074.

Cf. A057427, A218025.

Sequence in context: A240735 A057042 A063595 * A130082 A241377 A266750

Adjacent sequences: A316077 A316078 A316079 * A316081 A316082 A316083

Keyword

nonn,eigen

Author

Alois P. Heinz, Jun 23 2018

Status

approved