A226334 Number of nondecreasing -2..2 vectors of length n whose dot product with some other -2..2 vector equals n.

2, 14, 23, 67, 100, 202, 281, 479, 636, 971, 1243, 1770, 2205, 2980, 3630, 4725, 5654, 7140, 8415, 10381, 12082, 14614, 16823, 20027, 22840, 26817, 30331, 35204, 39531, 45416, 50668, 57705, 64010, 72330, 79815, 89575, 98384, 109730, 120005, 133111

Offset

1,1

Comments

Column 2 of A226340.

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: x*(2 + 12*x + 5*x^2 + 20*x^3 + 13*x^4 + 2*x^5 + 12*x^6 - 2*x^7 + x^9 - 2*x^10 - x^11 + x^12) / ((1 - x)^5*(1 + x)^4*(1 + x^2)^2).

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) + a(n-4) - a(n-5) - 4*a(n-6) + 4*a(n-7) + a(n-8) - a(n-9) + 2*a(n-10) - 2*a(n-11) - a(n-12) + a(n-13) for n>13.

(End)

Example

Some solutions for n=3:
.-1...-1...-1....0...-1...-2...-1...-2....1....1...-2...-1...-1...-1....1...-2
..1...-1....2....1....1...-1...-1...-1....1....2...-2....0...-1....0....1....1
..2....1....2....1....1....0....0....1....2....2....1....1....2....2....1....1

Crossrefs

Cf. A226340.

Sequence in context: A220274 A036433 A172048 * A109255 A285990 A174594

Adjacent sequences: A226331 A226332 A226333 * A226335 A226336 A226337

Keyword

nonn

Author

R. H. Hardin, Jun 04 2013

Status

approved