0,2

Generalized Pellian with second term equal to 4.

The generalized Pellian with second term equal to s has the terms a(n) = A000129(n)*s+A00129(n-1). The generating function is -(1+s*x-2*x)/(-1+2*x+x^2) . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 22 2007

A. F. Horadam, Pell Identities, Fibonacci Quarterly, Vol. 9, No. 3, 1971, pp. 245-252.

A. F. Horadam, Basic Properties of a Certain Generalized Sequence of Numbers, Fibonacci Quarterly, Vol. 3, No. 3, 1965, pp. 161-176.

A. F. Horadam, Special Properties of the Sequence W(a, b; p, q), Fibonacci Quarterly, Vol. 5, No. 5, 1967, pp. 424-434.

T. D. Noe, Table of n, a(n) for n=0..300

Index entries for sequences related to linear recurrences with constant coefficients

Tanya Khovanova, Recursive Sequences

a(n)=[ (3+sqrt(2))(1+sqrt(2))^n - (3-sqrt(2))(1-sqrt(2))^n ]/2*sqrt(2).

A048654(n) = 2P(n+2) - 3P(n+1), P(n) = Pell numbers (A000129) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Oct 27 2004

G.f.: (1+2*x)/(1-2*x-x^2). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 03 2008]

a(n)=binomial transform of 1,3,2,6,4,12 [From Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009]

with(combinat): a:=n->2*fibonacci(n-1, 2)+fibonacci(n, 2): seq(a(n), n=1..26); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2008

a=2; b=1; c=1; lst={b}; Do[c=a+b+c; AppendTo[lst, c]; a=b; b=c, {n, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Mar 23 2009]

Cf. A001333, A000129, A048655, A038761, A100525.

Sequence in context: A032288 A076859 A042833 this_sequence A122626 A135025 A070713

Adjacent sequences: A048651 A048652 A048653 this_sequence A048655 A048656 A048657

easy,nice,nonn

Barry E. Williams