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 A252976 T(n,k) = Number of n X k nonnegative integer arrays with upper left 0 and lower right n+k-5 and value increasing by 0 or 1 with every step right or down. 10
 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 4, 13, 18, 13, 4, 10, 61, 153, 153, 61, 10, 20, 192, 770, 1236, 770, 192, 20, 35, 483, 2859, 6997, 6997, 2859, 483, 35, 56, 1050, 8694, 30802, 46812, 30802, 8694, 1050, 56, 84, 2058, 22924, 112877, 248182, 248182, 112877, 22924, 2058 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,11 COMMENTS Table starts ..0....0......0.......1........4........10.........20..........35...........56 ..0....0......1......13.......61.......192........483........1050.........2058 ..0....1.....18.....153......770......2859.......8694.......22924........54272 ..1...13....153....1236.....6997.....30802.....112877......359550......1024773 ..4...61....770....6997....46812....248182....1100210.....4230324.....14477724 .10..192...2859...30802...248182...1592348....8528422....39423196....161160206 .20..483...8694..112877..1100210...8528422...54926890...303382053...1471499970 .35.1050..22924..359550..4230324..39423196..303382053..1988261908..11360377192 .56.2058..54272.1024773.14477724.161160206.1471499970.11360377192..75922639116 .84.3732.118057.2667554.44951694.593478797.6383377435.57644900961.447545856560 LINKS R. H. Hardin, Table of n, a(n) for n = 1..449 R. J. Mathar, Counting 2-way monotonic terrace forms over rectangular landscapes, vixra 1511.0225 (2015), subtable T_{n X m}(n+m-5). FORMULA Empirical for column k: k=1: a(n) = (1/6)*n^3 - 1*n^2 + (11/6)*n - 1 k=2: [polynomial of degree 6] k=3: [polynomial of degree 9] k=4: [polynomial of degree 12] k=5: [polynomial of degree 15] k=6: [polynomial of degree 18] k=7: [polynomial of degree 21] Empirical: with "n+k-3" instead of "n+k-5" T(n,k) = binomial(n+k,k) - 2, see A166810, A166812, A166813. EXAMPLE Some solutions for n=4, k=4: ..0..0..0..0....0..0..0..1....0..0..1..1....0..1..1..1....0..1..2..3 ..0..0..0..1....0..1..1..1....1..1..1..2....0..1..1..1....0..1..2..3 ..0..1..1..2....1..2..2..2....1..2..2..3....1..1..2..2....0..1..2..3 ..1..1..2..3....1..2..2..3....1..2..3..3....1..2..2..3....1..1..2..3 CROSSREFS Cf. A252876, A252930. Column 1 is A000292(n-3). Cf. A252970-A252975 (columns 2-7). Sequence in context: A042713 A154130 A041407 * A065564 A332377 A268720 Adjacent sequences: A252973 A252974 A252975 * A252977 A252978 A252979 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Dec 25 2014 STATUS approved

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Last modified December 2 11:06 EST 2022. Contains 358493 sequences. (Running on oeis4.)