A316079 Sequence shifts left seven places under Weigh transform with a(n) = signum(n) for n<7.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 11, 14, 19, 26, 35, 48, 65, 89, 122, 167, 230, 317, 438, 606, 840, 1167, 1622, 2260, 3151, 4398, 6148, 8601, 12046, 16888, 23697, 33283, 46783, 65814, 92654, 130539, 184039, 259639, 366533, 517749, 731781

Offset

0,11

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 * 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)))(7):
seq(a(n), n=0..51);

Crossrefs

Column k=7 of A316074.

Cf. A057427, A218024.

Sequence in context: A143065 A192660 A173692 * A091585 A032228 A091583

Adjacent sequences: A316076 A316077 A316078 * A316080 A316081 A316082

Keyword

nonn,eigen

Author

Alois P. Heinz, Jun 23 2018

Status

approved