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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 = 0..200 (corrected by R. H. Hardin, Jan 19 2019) 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) = (A000032(n + 3) - 2*sin(n*Pi/2) - 4*cos(n*Pi/2))/5. - Eric W. Weisstein, Apr 10 2018 a(n) = (Lucas(n+3) - (-1)^(floor(n/2))*(3+(-1)^n))/5. - G. C. Greubel, Apr 03 2019 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, 0, 40}] (* Eric W. Weisstein, Apr 10 2018 *) LinearRecurrence[{1, 0, 1, 1}, {0, 1, 3, 4, 5}, 40] (* Eric W. Weisstein, Apr 10 2018; amended for a(0) by Georg Fischer, Apr 03 2019 *) CoefficientList[Series[x*(1+x)^2/(1-x-x^3-x^4), {x, 0, 40}], x] (* Eric W. Weisstein, Apr 10 2018 *) PROG (PARI) my(x='x+O('x^40)); concat(, Vec(x*(1+x)^2/(1-x-x^3-x^4))) \\ G. C. Greubel, Apr 03 2019 (MAGMA) R:=PowerSeriesRing(Integers(), 40);  cat Coefficients(R!( x*(1+x)^2/(1-x-x^3-x^4) )); // G. C. Greubel, Apr 03 2019 (Sage) (x*(1+x)^2/(1-x-x^3-x^4)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 03 2019 (GAP) a:=[1, 3, 4, 5];; for n in [5..40] do a[n]:=a[n-1]+a[n-3]+a[n-4]; od; Concatenation(, a); # G. C. Greubel, Apr 03 2019 CROSSREFS Cf. A195978. Sequence in context: A195609 A117125 A000692 * A080552 A215176 A257041 Adjacent sequences:  A195968 A195969 A195970 * A195972 A195973 A195974 KEYWORD nonn,easy AUTHOR R. H. Hardin, Sep 25 2011 STATUS approved

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Last modified August 5 21:45 EDT 2020. Contains 336213 sequences. (Running on oeis4.)