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A188899
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Third row of array in A187617.
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4
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1, 5, 36, 281, 2245, 18061, 145601, 1174500, 9475901, 76455961, 616891945, 4977472781, 40161441636, 324048393905, 2614631600701, 21096536145301, 170220478472105, 1373448758774436, 11081871650713781, 89415697915538545, 721463601671126161, 5821234309893001301, 46969478172465070500, 378980086070257592201, 3057856106268358639861
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OFFSET
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0,2
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..400
N. Allegra, Exact solution of the 2d dimer model: Corner free energy, correlation functions and combinatorics, arXiv:1410.4131 [cond-mat.stat-mech], 2014. See Table 1.
Index entries for linear recurrences with constant coefficients, signature (11,-25,11,-1).
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FORMULA
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G.f.: (1-x)*(x^2-5*x+1)/(x^4-11*x^3+25*x^2-11*x+1). - Alois P. Heinz, Oct 28 2012
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MAPLE
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ft:=(m, n)->
2^(m*n/2)*mul( mul(
(cos(Pi*i/(n+1))^2+cos(Pi*j/(m+1))^2), j=1..m/2), i=1..n/2);
gt:=(m, n)->round(evalf(ft(m, n), 300));
tt:=[seq(gt(4, 2*n), n=0..10)];
# second Maple program:
a:= n-> (<<0|1|0|0>, <0|0|1|0>, <0|0|0|1>, <-1|11|-25|11>>^n.
<<1, 5, 36, 281>>)[1, 1]:
seq(a(n), n=0..30); # Alois P. Heinz, Oct 28 2012
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MATHEMATICA
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LinearRecurrence[{11, -25, 11, -1}, {1, 5, 36, 281}, 25] (* Jean-François Alcover, Jun 17 2018 *)
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PROG
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(PARI) x='x+O('x^200); Vec((1-x)*(x^2-5*x+1)/(x^4-11*x^3+25*x^2-11*x+1)) \\ Altug Alkan, Mar 23 2016
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CROSSREFS
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Bisection (odd part) of A005178. - Alois P. Heinz, Oct 28 2012
Sequence in context: A327091 A201351 A253470 * A052203 A332624 A027331
Adjacent sequences: A188896 A188897 A188898 * A188900 A188901 A188902
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane, Apr 13 2011
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STATUS
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approved
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