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 A195971 Number of n X 1 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,0,1,3,4 for x=0,1,2,3,4. 16
 0, 1, 3, 4, 5, 9, 16, 25, 39, 64, 105, 169, 272, 441, 715, 1156, 1869, 3025, 4896, 7921, 12815, 20736, 33553, 54289, 87840, 142129, 229971, 372100, 602069, 974169, 1576240, 2550409, 4126647, 6677056, 10803705, 17480761, 28284464, 45765225 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Every 0 is next to 0 2's, every 1 is next to 1 0's, every 2 is next to 2 1's, every 3 is next to 3 3's, every 4 is next to 4 4's. Column 1 of A195978. a(n) is the number of total dominating sets in the (n+1)-path graph. - Eric W. Weisstein, Apr 10 2018 LINKS R. H. Hardin, Table of n, a(n) for n = 1..200 Eric Weisstein's World of Mathematics, Path Graph Eric Weisstein's World of Mathematics, Total Dominating Set Index entries for linear recurrences with constant coefficients, signature (1, 0, 1, 1). FORMULA a(n) = a(n-1) + a(n-3) + a(n-4). G.f.: x*(1 + x)^2 / ((1 + x^2)*(1 - x - x^2)). - Colin Barker, Feb 17 2018 a(n) = (lucasl(n + 3) - 2*sin(n*Pi/2) - 4*cos(n*Pi/2))/5. - Eric W. Weisstein, Apr 10 2018 EXAMPLE All solutions for n=4:   0   0   1   1   0   0   0   0   0   1   0   0   0   0   1   1   0   1   0   0 MATHEMATICA Table[(LucasL[n + 3] - 2 Sin[n Pi/2] - 4 Cos[n Pi/2])/5, {n, 20}] (* Eric W. Weisstein, Apr 10 2018 *) LinearRecurrence[{1, 0, 1, 1}, {1, 3, 4, 5}, 20] (* Eric W. Weisstein, Apr 10 2018 *) CoefficientList[Series[(-1 - 2 x - x^2)/(-1 + x + x^3 + x^4), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 10 2018 *) CROSSREFS Sequence in context: A195609 A117125 A000692 * A080552 A215176 A257041 Adjacent sequences:  A195968 A195969 A195970 * A195972 A195973 A195974 KEYWORD nonn AUTHOR R. H. Hardin, Sep 25 2011 STATUS approved

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Last modified September 23 02:13 EDT 2018. Contains 315271 sequences. (Running on oeis4.)