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 A250755 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with nondecreasing x(i,j)-x(i,j-1) in the i direction and nondecreasing x(i,j)+x(i-1,j) in the j direction 15
 32, 72, 105, 129, 237, 332, 203, 423, 756, 1029, 294, 663, 1353, 2361, 3152, 402, 957, 2123, 4239, 7272, 9585, 527, 1305, 3066, 6663, 13089, 22197, 29012, 669, 1707, 4182, 9633, 20603, 40023, 67356, 87549, 828, 2163, 5471, 13149, 29814, 63063, 121593 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts .....32......72.....129.....203.....294......402......527......669......828 ....105.....237.....423.....663.....957.....1305.....1707.....2163.....2673 ....332.....756....1353....2123....3066.....4182.....5471.....6933.....8568 ...1029....2361....4239....6663....9633....13149....17211....21819....26973 ...3152....7272...13089...20603...29814....40722....53327....67629....83628 ...9585...22197...40023...63063...91317...124785...163467...207363...256473 ..29012...67356..121593..191723..277746...379662...497471...631173...780768 ..87549..203601..367839..580263..840873..1149669..1506651..1911819..2365173 .263672..613872.1109649.1751003.2537934..3470442..4548527..5772189..7141428 .793065.1847757.3341223.5273463.7644477.10454265.13702827.17390163.21516273 LINKS R. H. Hardin, Table of n, a(n) for n = 1..241 FORMULA Empirical: T(n,k) = (3*(k+1)*(5*k+4)*3^n - (8*k^2+8*k)*2^n + (5*k^2-7*k))/4 Empirical for column k: k=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (27*3^n-8*2^n-1)/2 k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (63*3^n-24*2^n+3)/2 k=3: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (114*3^n-48*2^n+12)/2 k=4: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (180*3^n-80*2^n+26)/2 k=5: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (261*3^n-120*2^n+45)/2 k=6: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (357*3^n-168*2^n+69)/2 k=7: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (468*3^n-224*2^n+98)/2 Empirical for row n: n=1: a(n) = (17/2)*n^2 + (29/2)*n + 9 n=2: a(n) = 27*n^2 + 51*n + 27 n=3: a(n) = (173/2)*n^2 + (329/2)*n + 81 n=4: a(n) = 273*n^2 + 513*n + 243 n=5: a(n) = (1697/2)*n^2 + (3149/2)*n + 729 n=6: a(n) = 2607*n^2 + 4791*n + 2187 n=7: a(n) = (15893/2)*n^2 + (29009/2)*n + 6561 EXAMPLE Some solutions for n=4 k=4 ..1..1..1..1..0....0..0..0..0..0....0..0..0..0..0....0..0..0..0..0 ..1..1..1..1..2....2..2..2..2..2....1..1..1..1..1....0..0..0..0..0 ..1..1..1..1..2....0..0..0..0..0....0..0..0..0..0....1..1..1..1..1 ..0..1..1..1..2....1..1..1..2..2....2..2..2..2..2....0..0..2..2..2 ..0..1..1..1..2....0..0..0..1..2....0..1..1..1..2....0..0..2..2..2 CROSSREFS Column 1 is A053152(n+3) Sequence in context: A228665 A101539 A106700 * A216427 A104026 A216417 Adjacent sequences:  A250752 A250753 A250754 * A250756 A250757 A250758 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 27 2014 STATUS approved

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Last modified September 18 13:54 EDT 2021. Contains 347527 sequences. (Running on oeis4.)