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 A250812 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 min(x(i,j),x(i-1,j)) in the j direction 15
 36, 100, 129, 225, 379, 432, 441, 873, 1315, 1389, 784, 1731, 3081, 4321, 4356, 1296, 3097, 6171, 10233, 13735, 13449, 2025, 5139, 11116, 20631, 32745, 42769, 41112, 3025, 8049, 18537, 37333, 66291, 102393, 131455, 124869, 4356, 12043, 29145, 62469 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ......36.....100.....225......441......784.....1296.....2025......3025 .....129.....379.....873.....1731.....3097.....5139.....8049.....12043 .....432....1315....3081.....6171....11116....18537....29145.....43741 ....1389....4321...10233....20631....37333....62469....98481....148123 ....4356...13735...32745....66291...120304...201741...318585....479845 ...13449...42769..102393...207831...377857...634509..1003089...1512163 ...41112..131455..315561...641571..1167796..1962717..3104985...4683421 ..124869..400681..963513..1961031..3572173..6007149..9507441..14345803 ..377676.1214695.2924265..5955891.10854424.18260061.28908345..43630165 .1139169.3669409.8840313.18013431.32839417.55258029.87498129.132077683 LINKS R. H. Hardin, Table of n, a(n) for n = 1..241 FORMULA Empirical: T(n,k) = (((5/12)*k^4 + (11/3)*k^3 + (157/12)*k^2 + (95/6)*k + 6)*3^n - ((1/2)*k^4 + (7/2)*k^3 + (23/2)*k^2 + (17/2)*k)*2^n + (1/4)*k^4 + 1*k^3 + (9/4)*k^2 - (1/2)*k)/2 Empirical for column k: k=1: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (39*3^n-24*2^n+3)/2 k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (126*3^n-99*2^n+20)/2 k=3: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (304*3^n-264*2^n+66)/2 k=4: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (620*3^n-570*2^n+162)/2 k=5: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (1131*3^n-1080*2^n+335)/2 k=6: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (1904*3^n-1869*2^n+618)/2 k=7: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3); a(n) = (3016*3^n-3024*2^n+1050)/2 Empirical for row n: n=1: a(n) = (1/4)*n^4 + (5/2)*n^3 + (37/4)*n^2 + 15*n + 9 n=2: a(n) = 1*n^4 + 10*n^3 + 37*n^2 + 54*n + 27 n=3: a(n) = (15/4)*n^4 + 36*n^3 + (527/4)*n^2 + (359/2)*n + 81 n=4: a(n) = 13*n^4 + 121*n^3 + 439*n^2 + 573*n + 243 n=5: a(n) = (171/4)*n^4 + 390*n^3 + (5627/4)*n^2 + (3575/2)*n + 729 n=6: a(n) = 136*n^4 + 1225*n^3 + 4402*n^2 + 5499*n + 2187 n=7: a(n) = (1695/4)*n^4 + 3786*n^3 + (54287/4)*n^2 + (33539/2)*n + 6561 EXAMPLE Some solutions for n=4 k=4 ..1..1..0..0..0....1..0..0..0..0....1..1..1..1..0....0..0..0..0..0 ..0..0..1..1..1....0..0..0..0..0....0..0..0..0..0....2..2..2..2..2 ..1..1..2..2..2....2..2..2..2..2....2..2..2..2..2....2..2..2..2..2 ..0..0..1..1..1....1..1..1..1..2....2..2..2..2..2....1..1..1..1..2 ..0..0..1..2..2....0..1..1..1..2....0..0..1..1..2....1..1..1..1..2 CROSSREFS Row 1 is A000537(n+2) Sequence in context: A306213 A114819 A137945 * A072413 A131605 A296204 Adjacent sequences: A250809 A250810 A250811 * A250813 A250814 A250815 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Nov 27 2014 STATUS approved

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Last modified June 14 13:28 EDT 2024. Contains 373400 sequences. (Running on oeis4.)