OFFSET
0,8
COMMENTS
This sequence is similar to Somos-5 (A006721). - Michael Somos, Aug 15 2014
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,2,0,0,0,-1).
FORMULA
G.f.: (1 - x^2 + x^3 - x^4 - x^5) / (1 - 2*x^2 + x^6). - Michael Somos, Aug 15 2014
a(2-n) = (-1)^(mod(n, 4) == 1) * a(n) for all n in Z. - Michael Somos, Aug 15 2014
a(2*n) = 1, a(2*n + 1) = A000045(n) for all n in Z. - Michael Somos, Aug 15 2014
a(n) = 2*a(n-2) - a(n-6) for all n in Z. - Michael Somos, Aug 15 2014
0 = a(n)*a(n+5) - a(n+1)*a(n+4) - a(n+2)*a(n+3) for all even n in Z. - Michael Somos, Aug 15 2014
0 = a(n)*a(n+5) - a(n+1)*a(n+4) + a(n+2)*a(n+3) for all odd n in Z. - Michael Somos, Aug 15 2014
EXAMPLE
G.f. = 1 + x^2 + x^3 + x^4 + x^5 + x^6 + 2*x^7 + x^8 + 3*x^9 + x^10 + ...
MAPLE
G := 1/(1-x^2)+x^3/(1-x^2-x^4); Gser := series(G, x = 0, 70); seq(coeff(Gser, x, n), n = 0 .. 65); # Emeric Deutsch, Jul 09 2007
MATHEMATICA
a[ n_] := If[ OddQ[n], Fibonacci[ Quotient[ n, 2]], 1]; (* Michael Somos, Aug 15 2014 *)
PROG
(PARI) {a(n) = if( n%2, fibonacci( n\2), 1)}; /* Michael Somos, Aug 15 2014 */
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Jun 14 2007
EXTENSIONS
More terms from Emeric Deutsch, Jul 09 2007
STATUS
approved