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
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
KEYWORD
sign,easy
AUTHOR
R. J. Mathar, Jan 31 2023
STATUS
approved