A360262 Determinant of the pentadiagonal symmetric nXn Toeplitz Matrix with a=b=1, c=3.

1, 1, 0, -4, 56, 177, 25, -248, 1536, 19448, 10025, 2313, -78584, 1525084, 2046000, 1990649, -12721279, 80406480, 282880000, 276053680, -672007599, 1449521681, 28914914000, 32747999676, 14429332456, -221875825343

Offset

0,4

Links

Table of n, a(n) for n=0..25.

J. Borowska, L. Lacinska, Recurrence form of determinant of a heptadiagonal symmetric Toeplitz matrix, J. Appl. Math. Comp. Mech. 13 (2014) 19-16, remark 1 with a=b=1, c=3.

Index entries for linear recurrences with constant coefficients, signature (-2,2,-6,54,243).

Formula

G.f. ( -1-3*x ) / ( (3*x-1)*(81*x^4+45*x^3+13*x^2+5*x+1) ).

a(n)= -2*a(n-1) +2*a(n-2) -6*a(n-3) +54*a(n-4) +243*a(n-5).

Crossrefs

Sequence in context: A143649 A168133 A189864 * A192845 A144138 A331776

Adjacent sequences: A360259 A360260 A360261 * A360263 A360264 A360265

Keyword

sign,easy

Author

R. J. Mathar, Jan 31 2023

Status

approved