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A252814 Number of n X 2 nonnegative integer arrays with upper left 0 and every value within 2 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down. 2
2, 6, 17, 40, 81, 147, 246, 387, 580, 836, 1167, 1586, 2107, 2745, 3516, 4437, 5526, 6802, 8285, 9996, 11957, 14191, 16722, 19575, 22776, 26352, 30331, 34742, 39615, 44981, 50872, 57321, 64362, 72030, 80361, 89392, 99161, 109707, 121070, 133291 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
W. Kuszmaul, Fast Algorithms for Finding Pattern Avoiders and Counting Pattern Occurrences in Permutations, arXiv preprint arXiv:1509.08216 [cs.DM], 2015-2017.
FORMULA
Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 - (1/24)*n^2 + (7/12)*n + 1.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(2 - 4*x + 7*x^2 - 5*x^3 + x^4) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
(End)
EXAMPLE
Some solutions for n=4:
..0..0....0..1....0..1....0..1....0..1....0..1....0..1....0..0....0..0....0..1
..0..1....0..1....1..2....1..2....0..1....0..1....1..2....1..1....1..1....1..2
..1..1....1..1....2..3....2..3....1..2....1..1....2..2....1..2....2..2....2..2
..2..2....1..2....2..3....3..4....2..2....2..2....3..3....1..2....2..3....2..2
CROSSREFS
Column 2 of A252820.
Sequence in context: A037261 A239234 A192707 * A072077 A229732 A130104
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 22 2014
STATUS
approved

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Last modified July 22 09:17 EDT 2024. Contains 374485 sequences. (Running on oeis4.)