A025267 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ...+ a(n-1)*a(1) for n >= 4.

1, -1, 1, 3, 4, 3, 4, 19, 60, 124, 214, 455, 1266, 3404, 7974, 17699, 42050, 107956, 276534, 680140, 1647872, 4082562, 10366604, 26363583, 66318590, 166265630, 420151570, 1070885100, 2734066540, 6964626146, 17739885228, 45334834067, 116258144838

Offset

1,4

References

A. Cayley, On the Porism of the In-and-circumscribed Polygon, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 4, 292-308 (see p. 300).

Links

Table of n, a(n) for n=1..33.

Formula

G.f.: (1-sqrt(1-4*x+8*x^2-12*x^3))/2.

Recurrence: n*a(n) = 2*(2*n-3)*a(n-1) - 8*(n-3)*a(n-2) + 6*(2*n-9)*a(n-3). - Vaclav Kotesovec, Jan 25 2015

Mathematica

nmax = 30; aa = ConstantArray[0, nmax]; aa[[1]] = 1; aa[[2]] = -1; aa[[3]] = 1; Do[aa[[n]] = Sum[aa[[k]] * aa[[n-k]], {k, 1, n-1}], {n, 4, nmax}]; aa (* Vaclav Kotesovec, Jan 25 2015 *)

Prog

(PARI) a(n)=polcoeff((1-sqrt(1-4*x+8*x^2-12*x^3+x*O(x^n)))/2, n)

Crossrefs

Sequence in context: A087275 A265305 A072942 * A223169 A201420 A244055

Adjacent sequences: A025264 A025265 A025266 * A025268 A025269 A025270

Keyword

sign

Author

Clark Kimberling

Extensions

Additional comments from Michael Somos, Apr 19, 2000

Status

approved