A202117 Number of -1..1 arrays of n elements with first, second and third differences also in -1..1.

3, 7, 13, 19, 27, 35, 47, 65, 91, 129, 185, 267, 387, 563, 821, 1199, 1753, 2565, 3755, 5499, 8055, 11801, 17291, 25337, 37129, 54411, 79739, 116859, 171261, 250991, 367841, 539093, 790075, 1157907, 1696991, 2487057, 3644955, 5341937, 7828985

Offset

1,1

Comments

Column 1 of A202124.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 2*a(n-1) -a(n-2) +a(n-3) -a(n-4) for n>8.

Empirical g.f.: x*(3 + x + 2*x^2 - 3*x^3 - 2*x^4 - 6*x^5 - 2*x^6 - 2*x^7) / ((1 - x)*(1 - x - x^3)). - Colin Barker, May 27 2018

Example

Some solutions for n=7:
..1....1....1....0....1....1....0....0....1....1...-1...-1...-1....1...-1....0
..1....0....1...-1....0....1...-1....1....1....1....0...-1...-1....0....0....0
..1...-1....1...-1....0....0...-1....1....1....1....0...-1....0....0....1....0
..1...-1....1....0....0...-1...-1....1....1....0....0...-1....1....0....1....0
..1....0....1....1....0...-1...-1....0....0...-1....0...-1....1....0....1....0
..1....1....1....1....0....0....0...-1...-1...-1....0...-1....0....0....1....0
..0....1....1....0...-1....1....1...-1...-1...-1....1...-1...-1....0....0....0

Crossrefs

Cf. A202124.

Sequence in context: A117679 A310265 A276215 * A100458 A193765 A000960

Adjacent sequences: A202114 A202115 A202116 * A202118 A202119 A202120

Keyword

nonn

Author

R. H. Hardin, Dec 11 2011

Status

approved