A188899 Third row of array in A187617.

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

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-François 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: A327091 A201351 A253470 * A052203 A371775 A332624

Adjacent sequences: A188896 A188897 A188898 * A188900 A188901 A188902

Keyword

nonn

Author

N. J. A. Sloane, Apr 13 2011

Status

approved