



1, 5, 3, 13, 19, 45, 83, 173, 339, 685, 1363, 2733, 5459, 10925, 21843, 43693, 87379, 174765, 349523, 699053, 1398099, 2796205, 5592403, 11184813, 22369619, 44739245, 89478483, 178956973, 357913939, 715827885, 1431655763, 2863311533, 5726623059
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OFFSET

0,2


COMMENTS

Also generalized kbonacci sequence a(n)=2*a(n2)a(n1).  Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Jun 30 2007
The kbonacci sequences are constructed using the formula a(n+k)=sum({i=1 to k1) a(n+i) where integers a(0) to a(k1) are given. The generalized kbonnacci sequences are built with the formula a(n+k) =sum({i=1 to k1}p(i)* a(n+i)), where integer coefficients p(1) to p(k1) and integers a(0) to a(k1) are given . The terms of such a sequence may be calculated by a formula such as: a(n>=k) = sum ({i =0 to k1} q(i) * r(i)^n) where r(0) to r(k1) are the roots (real or complex) of the equation x^k= sum {i=0 to i=k1}p(i)x^i) The coefficients q(i) (real or complex) may be calculated by the system of equations: {for p=0 to k1} sum( {(i=0 to k1} q(i)*r(i)^p)=a(p), first given terms of the sequence For this sequence, the roots of x^2=2*x1 are 1 and 2 The system of equations for q(0) and q(1) is q(0)+ q(1) = 1 q(0)2*q(1)= 5 which gives q(0)=7/3 and q(1)= 4/3 and then the first proposed formula.  Philippe LALLOUET (philip.lallouet(AT)wanadoo.fr), Jun 30 2007


LINKS

Table of n, a(n) for n=0..32.
Index entries for linear recurrences with constant coefficients, signature (1,2).


FORMULA

G.f. (1+6*x)/((1x)*(1+2*x)).
E.g.f. (7*exp(x)4*exp(2*x))/3.


MATHEMATICA

(74(2)^Range[0, 40])/3 (* or *) LinearRecurrence[{1, 2}, {1, 5}, 40] (* Harvey P. Dale, Feb 25 2012 *)


CROSSREFS

Cf. A083595.
Sequence in context: A085910 A093544 A082983 * A178497 A213750 A213774
Adjacent sequences: A083591 A083592 A083593 * A083595 A083596 A083597


KEYWORD

easy,sign


AUTHOR

Paul Barry, May 02 2003


STATUS

approved



