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%I #6 Jun 10 2024 00:17:16
%S 1,1,0,-4,56,177,25,-248,1536,19448,10025,2313,-78584,1525084,2046000,
%T 1990649,-12721279,80406480,282880000,276053680,-672007599,1449521681,
%U 28914914000,32747999676,14429332456,-221875825343
%N Determinant of the pentadiagonal symmetric nXn Toeplitz Matrix with a=b=1, c=3.
%H J. Borowska, L. Lacinska, <a href="https://doi.org/10.17512/jamcm.2014.4.03">Recurrence form of determinant of a heptadiagonal symmetric Toeplitz matrix</a>, J. Appl. Math. Comp. Mech. 13 (2014) 19-16, remark 1 with a=b=1, c=3.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-2,2,-6,54,243).
%F G.f. ( -1-3*x ) / ( (3*x-1)*(81*x^4+45*x^3+13*x^2+5*x+1) ).
%F a(n)= -2*a(n-1) +2*a(n-2) -6*a(n-3) +54*a(n-4) +243*a(n-5).
%K sign,easy
%O 0,4
%A _R. J. Mathar_, Jan 31 2023