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 A223680 T(n,k)=Number of nXk 0..1 arrays with rows and antidiagonals unimodal 11
 2, 4, 4, 7, 16, 8, 11, 49, 64, 16, 16, 121, 316, 256, 32, 22, 256, 1118, 2032, 1024, 64, 29, 484, 3177, 9822, 13045, 4096, 128, 37, 841, 7745, 35509, 85663, 83737, 16384, 256, 46, 1369, 16857, 105995, 384009, 744272, 537496, 65536, 512, 56, 2116, 33615, 275775 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....2.......4.........7.........11..........16...........22............29 ....4......16........49........121.........256..........484...........841 ....8......64.......316.......1118........3177.........7745.........16857 ...16.....256......2032.......9822.......35509.......105995........275775 ...32....1024.....13045......85663......384009......1363639.......4123210 ...64....4096.....83737.....744272.....4106403.....17068664......58944337 ..128...16384....537496....6458585....43632367....210660192.....821284360 ..256...65536...3450100...56030742...462307835...2577807779...11265254628 ..512..262144..22145617..486038270..4893189359..31402790284..152970187735 .1024.1048576.142149013.4215998078.51766786082.381690187059.2064772010660 LINKS R. H. Hardin, Table of n, a(n) for n = 1..480 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 4*a(n-1) k=3: a(n) = 7*a(n-1) -3*a(n-2) -5*a(n-3) +2*a(n-4) k=4: [order 9] k=5: [order 19] k=6: [order 36] k=7: [order 70] Empirical for row n: n=1: a(n) = (1/2)*n^2 + (1/2)*n + 1 n=2: a(n) = (1/4)*n^4 + (1/2)*n^3 + (5/4)*n^2 + 1*n + 1 n=3: a(n) = (23/360)*n^6 + (31/120)*n^5 + (17/9)*n^4 + (23/24)*n^3 + (917/360)*n^2 + (77/60)*n + 1 n=4: polynomial of degree 8 n=5: polynomial of degree 10 for n>2 n=6: polynomial of degree 12 for n>3 n=7: polynomial of degree 14 for n>4 EXAMPLE Some solutions for n=3 k=4 ..0..0..0..0....0..0..1..1....1..1..0..0....0..0..0..1....0..0..0..0 ..1..0..0..0....0..1..1..0....0..1..1..0....1..1..0..0....1..0..0..0 ..0..0..0..0....0..0..0..1....0..0..0..1....0..0..0..0....1..1..0..0 CROSSREFS Column 1 is A000079 Column 2 is A000302 Column 3 is A188868 Row 1 is A000124 Row 2 is A086601 Sequence in context: A188567 A262274 A223669 * A189264 A188992 A189617 Adjacent sequences: A223677 A223678 A223679 * A223681 A223682 A223683 KEYWORD nonn,tabl AUTHOR R. H. Hardin Mar 25 2013 STATUS approved

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Last modified August 3 18:16 EDT 2024. Contains 374899 sequences. (Running on oeis4.)