A316076 Sequence shifts left four places under Weigh transform with a(n) = signum(n) for n<4.

0, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 6, 8, 12, 18, 26, 39, 58, 88, 133, 202, 308, 472, 725, 1116, 1725, 2669, 4141, 6437, 10027, 15643, 24448, 38265, 59979, 94143, 147953, 232799, 366725, 578311, 912913, 1442503, 2281429, 3611406, 5721528, 9071789, 14394837

Offset

0,8

Links

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

Formula

G.f.: x + x^2 + x^3 + x^4 * 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)))(4):
seq(a(n), n=0..45);

Crossrefs

Column k=4 of A316074.

Cf. A057427, A218021.

Sequence in context: A017912 A102543 A173383 * A368746 A325832 A068598

Adjacent sequences: A316073 A316074 A316075 * A316077 A316078 A316079

Keyword

nonn,eigen

Author

Alois P. Heinz, Jun 23 2018

Status

approved