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 A098485 Triangle T(m,k) read by rows, where T(m,k) is the number of ways in which 1<=k<=m positions can be picked in an m X m square array such that their adjacency graph consist of a single component. Two positions (s,t),(u,v) are considered as adjacent, if max(abs(s-u),abs(t-v))<=1. 10
 1, 4, 6, 9, 20, 48, 16, 42, 132, 419, 25, 72, 256, 973, 3682, 36, 110, 420, 1747, 7484, 31992, 49, 156, 624, 2741, 12562, 58620, 273556, 64, 210, 868, 3955, 18916, 92912, 462104, 2927505, 81, 272, 1152, 5389, 26546, 134868, 697836, 3644935, 19082018 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Number of ways to mark the numbers on a square board on a lottery play slip such that one connected graphic pattern is formed. For the lottery "mark 6 numbers of 49 on a 7X7 grid of numbers" that is played in many countries, there are T(7,6)=58620 (out of binomial(49,6)=13983816) different combinations of 6 numbers whose graphic pattern on the board forms one connected component. LINKS John Burkardt, GRAFPACK Graph Computations. EXAMPLE a(5)=T(3,2)=20 because there are 20 ways to mark two positions in a 3 X 3 square grid such that the two picked positions are either row-wise, column-wise or diagonally adjacent: XX0...X00...X00...0XX...0X0...0X0...0X0...00X...00X...000 000...X00...0X0...000...X00...0X0...00X...0X0...00X...XX0 000...000...000...000...000...000...000...000...000...000 ......................................................... 000...000...000...000...000...000...000...000...000...000 000...X00...0X0...000...X00...0X0...00X...0X0...00X...0XX XX0...X00...X00...0XX...0X0...0X0...0X0...00X...00X...000 PROG FORTRAN program: See link. CROSSREFS Cf. A090642, A098487 (selections where all marks are isolated from each other), A291716, A291717, A291718, A292152, A292153, A292154, A292155, A292156. Sequence in context: A220144 A152002 A171127 * A293399 A120712 A115698 Adjacent sequences:  A098482 A098483 A098484 * A098486 A098487 A098488 KEYWORD nonn,tabl AUTHOR Hugo Pfoertner, Sep 14 2004 STATUS approved

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Last modified January 18 13:09 EST 2019. Contains 319271 sequences. (Running on oeis4.)