A316075 Sequence shifts left three places under Weigh transform with a(n) = signum(n) for n<3.

0, 1, 1, 1, 1, 1, 2, 2, 3, 5, 7, 10, 17, 26, 40, 65, 104, 166, 272, 442, 720, 1186, 1954, 3222, 5346, 8881, 14778, 24668, 41254, 69088, 115959, 194925, 328123, 553200, 933944, 1578614, 2671656, 4526654, 7677736, 13035809, 22154806, 37687152, 64165838

Offset

0,7

Links

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

Formula

G.f.: x + x^2 + x^3 * 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)))(3):
seq(a(n), n=0..42);

Crossrefs

Column k=3 of A316074.

Cf. A057427, A218020.

Sequence in context: A173696 A120412 A022864 * A322429 A039894 A133225

Adjacent sequences: A316072 A316073 A316074 * A316076 A316077 A316078

Keyword

nonn,eigen

Author

Alois P. Heinz, Jun 23 2018

Status

approved