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A252816 Number of n X 4 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. 1
7, 40, 187, 684, 2078, 5490, 13015, 28299, 57338, 109549, 199168, 347035, 582831, 947837, 1498290, 2309416, 3480225, 5139158, 7450681, 10622926, 14916484, 20654460, 28233905, 38138745, 50954332, 67383747, 88265990, 114596197 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = (1/8064)*n^8 + (1/288)*n^7 + (103/2880)*n^6 + (17/90)*n^5 + (703/1152)*n^4 + (451/288)*n^3 + (2869/3360)*n^2 + (209/120)*n + 2.
Conjectures from Colin Barker, Dec 06 2018: (Start)
G.f.: x*(7 - 23*x + 79*x^2 - 147*x^3 + 176*x^4 - 138*x^5 + 67*x^6 - 18*x^7 + 2*x^8) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)
EXAMPLE
Some solutions for n=4:
..0..0..1..2....0..1..1..1....0..1..2..3....0..0..1..2....0..0..1..1
..1..1..2..3....0..1..1..2....1..2..3..3....1..1..1..2....1..1..1..2
..1..1..2..3....1..2..2..3....1..2..3..3....2..2..2..3....1..2..2..3
..1..2..3..4....1..2..3..4....2..3..3..4....2..3..3..4....1..2..3..4
CROSSREFS
Column 4 of A252820.
Sequence in context: A365373 A263473 A055282 * A093737 A268402 A351529
KEYWORD
nonn
AUTHOR
R. H. Hardin, Dec 22 2014
STATUS
approved

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Last modified July 14 14:54 EDT 2024. Contains 374318 sequences. (Running on oeis4.)