OFFSET
2,1
LINKS
FORMULA
a(n) = 2*(((sqrt(7)+sqrt(3))/2)^n + ((sqrt(7)-sqrt(3))/2)^n)^2.
G.f.: 2*x^2*(25-38*x+7*x^2)/((1-x)*(1-5*x+x^2)).
From Seiichi Manyama, Feb 14 2021: (Start)
a(n) = sqrt( Product_{j=1..n} Product_{k=1..3} (4*sin((2*j-1)*Pi/(2*n))^2 + 4*sin((2*k-1)*Pi/3)^2) ).
a(n) = 5*a(n-1) - a(n-2) - 12. (End)
a(n) = 6*A054493(n-1) + 8. - Peter Bala, May 17 2025
E.g.f.: 4*exp(x)*(1 + exp(3*x/2)*cosh(sqrt(21)*x/2)) - 8 - 14*x. - Stefano Spezia, Apr 04 2026
PROG
(PARI) Vec(2*x^2*(25-38*x+7*x^2)/((1-x)*(1-5*x+x^2))+O(x^66)) \\ Joerg Arndt, Nov 03 2013
(PARI) default(realprecision, 120);
a(n) = round(sqrt(prod(j=1, n, prod(k=1, 3, 4*sin((2*j-1)*Pi/(2*n))^2+4*sin((2*k-1)*Pi/3)^2)))); \\ Seiichi Manyama, Feb 14 2021
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Sergey Perepechko, Nov 03 2013
STATUS
approved