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A188899 Third row of array in A187617. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

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).

FORMULA

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

MAPLE

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

MATHEMATICA

LinearRecurrence[{11, -25, 11, -1}, {1, 5, 36, 281}, 25] (* Jean-Fran├žois Alcover, Jun 17 2018 *)

PROG

(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

CROSSREFS

Bisection (odd part) of A005178. - Alois P. Heinz, Oct 28 2012

Sequence in context: A285392 A201351 A253470 * A052203 A027331 A255489

Adjacent sequences:  A188896 A188897 A188898 * A188900 A188901 A188902

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Apr 13 2011

STATUS

approved

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Last modified February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)