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 A252823 Number of n X 3 nonnegative integer arrays with upper left 0 and every value within 3 of its city block distance from the upper left and every value increasing by 0 or 1 with every step right or down. 1
 4, 18, 81, 340, 1238, 3891, 10761, 26764, 60988, 129236, 257653, 487744, 883142, 1538541, 2591269, 4236040, 6743492, 10483190, 15951849, 23807612, 34911302, 50375655, 71623633, 100457012, 139136540, 190475064, 257945133, 345802696 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 FORMULA Empirical: a(n) = (1/90720)*n^9 + (1/2520)*n^8 + (19/3780)*n^7 + (1/45)*n^6 + (157/4320)*n^5 + (31/180)*n^4 + (28507/45360)*n^3 + (769/2520)*n^2 + (1783/630)*n. Conjectures from Colin Barker, Dec 06 2018: (Start) G.f.: x*(4 - 22*x + 81*x^2 - 140*x^3 + 163*x^4 - 137*x^5 + 75*x^6 - 23*x^7 + 3*x^8) / (1 - x)^10. a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>10. (End) EXAMPLE Some solutions for n=4: ..0..0..0....0..0..1....0..0..1....0..0..1....0..0..0....0..0..0....0..0..1 ..0..1..1....1..1..2....0..1..2....1..1..2....0..1..1....0..0..0....0..0..1 ..1..2..2....2..2..3....1..1..2....2..2..3....0..1..2....0..0..1....1..1..2 ..2..2..3....3..3..4....1..1..2....2..3..3....1..2..3....0..1..2....1..2..3 CROSSREFS Column 3 of A252828. Sequence in context: A063881 A264004 A282708 * A264191 A257060 A181610 Adjacent sequences: A252820 A252821 A252822 * A252824 A252825 A252826 KEYWORD nonn AUTHOR R. H. Hardin, Dec 22 2014 STATUS approved

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Last modified August 12 09:11 EDT 2024. Contains 375085 sequences. (Running on oeis4.)