A201081 Number of -1..1 arrays of n elements with first and second differences also in -1..1.

3, 7, 13, 25, 47, 89, 169, 321, 609, 1155, 2191, 4157, 7887, 14963, 28387, 53855, 102173, 193841, 367751, 697689, 1323641, 2511185, 4764169, 9038483, 17147623, 32532117, 61719263, 117092515, 222145507, 421449879, 799566029, 1516920201

Offset

1,1

Comments

Column 1 of A201088.

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).

Empirical g.f.: x*(3 + 2*x + x^2)*(1 + 3*x^2 - 2*x^3 + x^4) / ((1 - x)^3*(1 + x + x^2)^2). - Colin Barker, Feb 15 2018

Example

Some solutions for n=10:
..1....1....1...-1....1....0....0...-1....1....1....1....1....0....0....0...-1
..1....0....0...-1....0....0...-1...-1....0....0....1....0...-1....1....1...-1
..0...-1....0....0....0...-1...-1....0...-1...-1....1...-1...-1....1....1....0
.-1...-1....0....0....1...-1....0....1...-1...-1....0...-1....0....1....1....0
.-1...-1....0....1....1....0....0....1....0...-1....0....0....1....0....1....0
.-1...-1...-1....1....0....0...-1....0....0...-1...-1....0....1...-1....1...-1
..0...-1...-1....1....0....0...-1...-1....0...-1...-1....0....0...-1....1...-1
..0....0...-1....0....0....1...-1...-1....0...-1....0....0....0...-1....1...-1
..0....0....0....0....1....1....0...-1...-1....0....0....0....0...-1....0....0
..1....0....1...-1....1....1....1...-1...-1....1...-1....1...-1...-1....0....0

Crossrefs

Sequence in context: A269832 A341579 A336726 * A017994 A218199 A275788

Adjacent sequences: A201078 A201079 A201080 * A201082 A201083 A201084

Keyword

nonn

Author

R. H. Hardin, Nov 26 2011

Status

approved