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

Author

N. J. A. Sloane, Apr 13 2011

Keywords

• nonn

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).

Crossrefs

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

Programs

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 *)

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

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