The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 7 03:31 EST 2021. Contains 349567 sequences. (Running on oeis4.)