A316077 Sequence shifts left five places under Weigh transform with a(n) = signum(n) for n<5.

0, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 7, 10, 14, 20, 28, 40, 58, 84, 121, 176, 257, 376, 552, 812, 1196, 1767, 2615, 3877, 5757, 8562, 12751, 19018, 28400, 42461, 63554, 95234, 142845, 214473, 322310, 484793, 729797, 1099509, 1657761, 2501299, 3776681

Offset

0,9

Links

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

Formula

G.f.: x + x^2 + x^3 + x^4 + x^5 * 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)))(5):
seq(a(n), n=0..47);

Crossrefs

Column k=5 of A316074.

Cf. A057427, A218022.

Sequence in context: A173674 A018128 A032189 * A186425 A327662 A034395

Adjacent sequences: A316074 A316075 A316076 * A316078 A316079 A316080

Keyword

nonn,eigen

Author

Alois P. Heinz, Jun 23 2018

Status

approved