The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 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) -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 Adjacent sequences: A255989 A255990 A255991 * A255993 A255994 A255995 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Mar 13 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 5 03:48 EST 2023. Contains 360082 sequences. (Running on oeis4.)