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 A256816 T(n,k)=Number of length n+k 0..1 arrays with at most two downsteps in every k consecutive neighbor pairs 10
 4, 8, 8, 16, 16, 16, 32, 32, 32, 32, 63, 64, 64, 64, 64, 120, 124, 128, 128, 128, 128, 219, 229, 245, 256, 256, 256, 256, 382, 402, 442, 484, 512, 512, 512, 512, 638, 673, 753, 856, 956, 1024, 1024, 1024, 1024, 1024, 1080, 1220, 1424, 1656, 1888, 2048, 2048, 2048 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Table starts ....4....8...16....32....63...120...219...382....638...1024...1586...2380 ....8...16...32....64...124...229...402...673...1080...1670...2500...3638 ...16...32...64...128...245...442...753..1220...1894...2836...4118...5824 ...32...64..128...256...484...856..1424..2249...3402...4965...7032...9710 ...64..128..256...512...956..1656..2693..4158...6153...8792..12202..16524 ..128..256..512..1024..1888..3204..5088..7677..11120..15579..21230..28264 ..256..512.1024..2048..3728..6192..9613.14168..20075..27566..36888..48304 ..512.1024.2048..4096..7362.11955.18104.26117..36218..48738..64024..82440 .1024.2048.4096..8192.14539.23088.34013.47858..65130..86008.110976.140536 .2048.4096.8192.16384.28712.44617.63928.87338.116104.150906.191620.238932 LINKS R. H. Hardin, Table of n, a(n) for n = 1..9999 FORMULA Empirical for column k: k=1: a(n) = 2*a(n-1) k=2: a(n) = 2*a(n-1) k=3: a(n) = 2*a(n-1) k=4: a(n) = 2*a(n-1) k=5: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -a(n-4) +2*a(n-5) -a(n-6) k=6: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -a(n-4) +3*a(n-6) -2*a(n-7) -6*a(n-9) +4*a(n-10) k=7: [order 15] Empirical for row n: n=1: a(n) = (1/120)*n^5 + (1/8)*n^3 + (1/2)*n^2 + (41/30)*n + 2 n=2: a(n) = (1/120)*n^5 + (1/24)*n^4 + (3/8)*n^3 - (1/24)*n^2 + (277/60)*n + 3 n=3: a(n) = (1/120)*n^5 + (1/12)*n^4 + (31/24)*n^3 - (31/12)*n^2 + (66/5)*n + 4 n=4: [polynomial of degree 5] for n>2 n=5: [polynomial of degree 5] for n>3 n=6: [polynomial of degree 5] for n>4 n=7: [polynomial of degree 5] for n>5 EXAMPLE Some solutions for n=4 k=4 ..1....1....0....0....0....0....1....0....0....0....0....0....1....0....0....1 ..0....0....1....1....0....1....0....1....1....0....0....0....1....0....0....1 ..1....1....0....1....0....0....1....0....1....1....1....1....0....1....0....1 ..0....1....1....1....0....1....1....1....1....1....0....0....1....1....0....0 ..0....1....0....0....1....1....1....1....0....0....1....1....1....1....0....0 ..0....1....1....0....1....1....0....0....0....1....0....0....0....1....0....1 ..0....0....1....0....1....1....1....0....0....1....1....1....0....0....0....0 ..0....1....0....1....1....1....0....1....0....1....0....1....0....1....0....1 CROSSREFS Column 1 is A000079(n+1) Column 2 is A000079(n+2) Column 3 is A000079(n+3) Column 4 is A000079(n+4) Row 1 is A006261(n+1) Sequence in context: A114027 A005877 A144174 * A098354 A209382 A298119 Adjacent sequences:  A256813 A256814 A256815 * A256817 A256818 A256819 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Apr 10 2015 STATUS approved

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Last modified December 5 22:37 EST 2019. Contains 329782 sequences. (Running on oeis4.)