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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A218354 T(n,k) = Hilltop maps: number of nXk binary arrays indicating the locations of corresponding elements not exceeded by any horizontal or vertical neighbor in a random 0..1 n X k array. 16
 1, 3, 3, 5, 11, 5, 9, 41, 41, 9, 17, 149, 291, 149, 17, 31, 547, 2069, 2069, 547, 31, 57, 2007, 14811, 28661, 14811, 2007, 57, 105, 7361, 105913, 401253, 401253, 105913, 7361, 105, 193, 27001, 757305, 5609569, 10982565, 5609569, 757305, 27001, 193, 355 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Andrew Howroyd, May 10 2017: (Start) Number of n X k binary matrices with every 1 vertically or horizontally adjacent to some 0. Number of dominating sets in the grid graph P_n X P_k. (End) LINKS R. H. Hardin, Table of n, a(n) for n = 1..198 Eric Weisstein's World of Mathematics, Grid Graph Eric Weisstein's World of Mathematics, Dominating Set Wikipedia, Dominating Set FORMULA Empirical for column k: k=1: a(n) = a(n-1) +a(n-2) +a(n-3). k=2: a(n) = 3*a(n-1) +2*a(n-2) +2*a(n-3) -a(n-4) -a(n-5). k=3: a(n) = 6*a(n-1) +5*a(n-2) +22*a(n-3) +7*a(n-4) +8*a(n-5) -18*a(n-6) -20*a(n-7) -a(n-8) +4*a(n-9) +3*a(n-10) +a(n-12). Column k=1 for an underlying 0..z array: a(n) = sum(i=1..2z+1){a(n-i)} z=1,2,3,4 EXAMPLE Table starts ....1.......3...........5..............9.................17 ....3......11..........41............149................547 ....5......41.........291...........2069..............14811 ....9.....149........2069..........28661.............401253 ...17.....547.......14811.........401253...........10982565 ...31....2007......105913........5609569..........300126903 ...57....7361......757305.......78394141.........8199377227 ..105...27001.....5415209.....1095695529.......224032447213 ..193...99043....38722037....15314367301......6121258910011 ..355..363299...276885777...214044940145....167250519310183 ..653.1332617..1979899795..2991651891557...4569773233045519 .1201.4888173.14157473937.41813576818545.124859601874166153 ... Some solutions for n=3 k=4 ..1..0..1..1....1..1..1..0....1..1..1..0....1..0..1..1....1..0..1..1 ..1..0..1..0....1..0..1..0....0..0..1..0....1..0..1..1....1..1..0..1 ..0..0..1..0....1..1..0..1....0..1..1..1....1..1..1..1....1..1..1..0 CROSSREFS Columns 1-7 are A000213(n+1), A218348, A218349, A218350, A218351, A218352, A218353. Diagonal is A133515. Cf. A089934 (independent vertex sets), A210662 (matchings). Sequence in context: A072337 A335056 A132751 * A286514 A235859 A279790 Adjacent sequences:  A218351 A218352 A218353 * A218355 A218356 A218357 KEYWORD nonn,tabl AUTHOR R. H. Hardin, Oct 26 2012 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 January 23 08:11 EST 2021. Contains 340385 sequences. (Running on oeis4.)