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A255992 T(n,k)=Number of length n+k 0..1 arrays with at most one downstep in every k consecutive neighbor pairs 11
4, 8, 8, 15, 16, 16, 26, 28, 32, 32, 42, 45, 53, 64, 64, 64, 68, 80, 100, 128, 128, 93, 98, 114, 144, 188, 256, 256, 130, 136, 156, 196, 256, 354, 512, 512, 176, 183, 207, 257, 337, 451, 667, 1024, 1024, 232, 240, 268, 328, 428, 568, 796, 1256, 2048, 2048, 299, 308 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
....4....8...15...26...42...64...93..130..176..232..299..378..470..576...697
....8...16...28...45...68...98..136..183..240..308..388..481..588..710...848
...16...32...53...80..114..156..207..268..340..424..521..632..758..900..1059
...32...64..100..144..196..257..328..410..504..611..732..868.1020.1189..1376
...64..128..188..256..337..428..530..644..771..912.1068.1240.1429.1636..1862
..128..256..354..451..568..705..854.1016.1192.1383.1590.1814.2056.2317..2598
..256..512..667..796..945.1134.1352.1584.1831.2094.2374.2672.2989.3326..3684
..512.1024.1256.1413.1574.1797.2088.2419.2766.3130.3512.3913.4334.4776..5240
.1024.2048.2365.2510.2645.2848.3175.3606.4090.4592.5113.5654.6216.6800..7407
.2048.4096.4454.4448.4476.4560.4824.5294.5912.6598.7304.8031.8780.9552.10348
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) -a(n-2) +2*a(n-3) -a(n-4)
k=4: a(n) = 2*a(n-1) -a(n-2) +3*a(n-4) -2*a(n-5)
k=5: a(n) = 2*a(n-1) -a(n-2) +4*a(n-5) -3*a(n-6)
k=6: a(n) = 2*a(n-1) -a(n-2) +5*a(n-6) -4*a(n-7)
k=7: a(n) = 2*a(n-1) -a(n-2) +6*a(n-7) -5*a(n-8)
Empirical for row n:
n=1: a(n) = (1/6)*n^3 + (1/2)*n^2 + (4/3)*n + 2
n=2: a(n) = (1/6)*n^3 + n^2 + (23/6)*n + 3
n=3: a(n) = (1/6)*n^3 + (3/2)*n^2 + (31/3)*n + 4
n=4: a(n) = (1/6)*n^3 + 2*n^2 + (143/6)*n + 6 for n>2
n=5: a(n) = (1/6)*n^3 + (5/2)*n^2 + (145/3)*n + 12 for n>3
n=6: a(n) = (1/6)*n^3 + 3*n^2 + (533/6)*n + 28 for n>4
n=7: a(n) = (1/6)*n^3 + (7/2)*n^2 + (454/3)*n + 64 for n>5
EXAMPLE
Some solutions for n=4 k=4
..1....1....0....0....0....0....0....1....0....0....1....0....1....0....0....0
..1....0....0....1....1....0....0....1....1....0....1....0....1....0....0....1
..1....0....1....1....1....0....1....0....0....0....1....1....0....1....0....1
..1....1....0....1....0....1....1....0....0....0....0....1....0....0....1....1
..0....1....0....0....0....1....1....1....0....1....1....1....1....0....1....1
..1....1....0....1....1....0....1....1....0....0....1....1....1....0....1....1
..1....0....0....1....1....1....1....1....1....1....1....0....1....0....1....0
..1....1....1....1....0....1....0....1....0....1....0....1....0....0....1....1
CROSSREFS
Column 1 is A000079(n+1)
Column 2 is A000079(n+2)
Column 3 is A118870(n+3)
Row 1 is A000125(n+1)
Sequence in context: A333288 A159786 A083744 * A273572 A273779 A114027
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 13 2015
STATUS
approved

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Last modified April 16 05:35 EDT 2024. Contains 371697 sequences. (Running on oeis4.)