OFFSET
0,3
COMMENTS
Also binomial transform of Pell(n)(1-(-1)^n)/2.
LINKS
Index entries for linear recurrences with constant coefficients, signature (4,0,-8,4).
FORMULA
G.f.: x(1-2x)/((1-2*x^2)*(1-4*x+2*x^2));
a(n) = (sqrt(2)/8)*((2+sqrt(2))^n - (2-sqrt(2))^n + (sqrt(2))^n - (-sqrt(2))^n).
E.g.f.: (exp(x) * cosh(x) * sinh(sqrt(2)*x)) / sqrt(2). - Amiram Eldar, Jan 15 2026
MATHEMATICA
LinearRecurrence[{4, 0, -8, 4}, {0, 1, 2, 8}, 30] (* Harvey P. Dale, Jan 01 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 23 2004
STATUS
approved