OFFSET
1,1
LINKS
Index entries for linear recurrences with constant coefficients, signature (19, -76, 76, -19, 1)
FORMULA
a(n) = 19*a(n-1) - 76*a(n-2) + 76*a(n-3) - 19*a(n-4) + a(n-5).
a(n) = 18*a(n-1) - 58*a(n-2) + 18*a(n-3) - a(n-4) + 144.
From Vaclav Kotesovec, Feb 14 2021: (Start)
G.f.: 4*(4 - 67*x + 197*x^2 - 107*x^3 + 9*x^4) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)).
a(n) = 6 + 4*(2 + sqrt(3))^n + 4*(2 - sqrt(3))^n + (7 + 4*sqrt(3))^n + (7 - 4*sqrt(3))^n. (End)
MATHEMATICA
Table[6 + 4 (2 + Sqrt[3])^n + 4 (2 - Sqrt[3])^n + (7 + 4 Sqrt[3])^n + (7 - 4 Sqrt[3])^n, {n, 1, 20}] // FullSimplify (* Vaclav Kotesovec, Feb 14 2021 *)
PROG
(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 4, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/4)^2))));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 14 2021
STATUS
approved