A360261 Determinant of the pentadiagonal symmetric n X n Toeplitz Matrix with a=b=1, c=2.

1, 1, 0, -1, 7, 32, 9, 1, -32, 495, 567, 288, -935, 3025, 15840, 9503, 2023, -29920, 236457, 312481, 304096, -639153, 1252503, 7566624, 7396345, 2283121, -20452896, 108556415, 167727175, 236683040, -376631991, 491819329, 3473805280, 5032011951, 2018956023, -12052223712, 47535816601

Offset

0,5

Comments

For pentadiagonal a=2, b=c=1 the determinants are 1, 2, 3, 4, 4, 4, 3, 2, 1, 0, 0, 0, ... with period 12.

For pentadiagonal a=b=c=1 the determinants are 1,1,0,0,0,1,... with period 5.

Links

Table of n, a(n) for n=0..36.

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=2.

Index entries for linear recurrences with constant coefficients, signature (-1,1,-2,8,32).

Formula

G.f.: ( -1-2*x ) / ( (2*x-1)*(16*x^4+12*x^3+5*x^2+3*x+1) ).

a(n) = -a(n-1) +a(n-2) -2*a(n-3) +8*a(n-4) +32*a(n-5).

Crossrefs

Cf. A071534 (a=c=1, b=2).

Sequence in context: A101329 A193637 A214490 * A164819 A067811 A044084

Adjacent sequences: A360258 A360259 A360260 * A360262 A360263 A360264

Keyword

sign,easy

Author

R. J. Mathar, Jan 31 2023

Status

approved