VOOZH about

URL: https://oeis.org/A252932

⇱ A252932 - OEIS

login
A252932
Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 3 of its king move distance from the upper left and every value increasing by 0 or 1 with every step right, diagonally se or down.
1
2, 5, 13, 34, 83, 176, 329, 558, 879, 1308, 1861, 2554, 3403, 4424, 5633, 7046, 8679, 10548, 12669, 15058, 17731, 20704, 23993, 27614, 31583, 35916, 40629, 45738, 51259, 57208, 63601, 70454, 77783, 85604, 93933, 102786, 112179, 122128, 132649, 143758
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (8/3)*n^3 - 18*n^2 + (145/3)*n - 42 for n>2.
Conjectures from Colin Barker, Dec 07 2018: (Start)
G.f.: x*(2 - 3*x + 5*x^2 + 4*x^3 + 7*x^4 + x^5) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
(End)
EXAMPLE
Some solutions for n=4:
..0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..1....0..0....0..0
..1..1....1..1....1..1....1..1....0..1....0..1....0..1....0..1....0..0....0..0
..1..1....2..2....2..2....1..2....1..1....0..1....0..1....0..1....0..1....0..0
..1..1....2..2....3..3....2..2....2..2....1..1....0..1....1..1....0..1....0..0
CROSSREFS
Column 2 of A252938.
Sequence in context: A104589 A154101 A122024 * A318234 A371426 A027931
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 24 2014
STATUS
approved