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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
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 A354455 A209382
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 10 2015
STATUS
approved

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Last modified July 20 17:32 EDT 2024. Contains 374459 sequences. (Running on oeis4.)