OFFSET
0,3
COMMENTS
FORMULA
G.f.: (1-3x-x^2-sqrt(1-2x-x^2+6x^3+5x^4))/(2x(1-x-x^2));
G.f.: 1/(1-x(1+x)/(1-x/(1+x/(1-x(1+x)/(1-x/(1+x/(1-... continued fraction).
Conjecture: (n+1)*a(n) +n*a(n-1) +12*(-n+1)*a(n-2) +3*(3*n-8)*a(n-3) +6*(6*n-23)*a(n-4) +11*(-n+2)*a(n-5) +(-49*n+253)*a(n-6) +20*(-n+6)*a(n-7)=0. - R. J. Mathar, Jan 12 2013
EXAMPLE
G.f. = 1 + x + 3*x^2 + 6*x^3 + 12*x^4 + 22*x^5 + 37*x^6 + ... - Michael Somos, Jul 11 2024
MATHEMATICA
a[ n_] := SeriesCoefficient[2*(1-x)/(1-3*x-x^2 + Sqrt[1-2*x-x^2+6*x^3+5*x^4]), {x, 0, n}]; (* Michael Somos, Jul 11 2024 *)
PROG
(PARI) {a(n) = polcoeff(2*(1-x)/(1-3*x-x^2 + sqrt(1-2*x-x^2+6*x^3+5*x^4 + x*O(x^n))), n)}; /* Michael Somos, Jul 11 2024 */
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, Mar 05 2010
STATUS
approved