

A155046


List of pairs: first pair is (1,1); then follow (x,y) with (x+2y, x+y).


2



1, 1, 3, 2, 7, 5, 17, 12, 41, 29, 99, 70, 239, 169, 577, 408, 1393, 985, 3363, 2378, 8119, 5741, 19601, 13860, 47321, 33461, 114243, 80782, 275807, 195025, 665857, 470832, 1607521, 1136689, 3880899, 2744210, 9369319, 6625109, 22619537, 15994428
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OFFSET

1,3


COMMENTS

Sequence of x: A078057(n); sequence of y: A000129(n).  R. J. Mathar, Feb 19 2009
a(2k+1)^2  2*a(2k+2)^2 = +1.  Vincenzo Librandi, Mar 14 2012
List of pairs (a, b) such that (a, b*sqrt(2)) = (1 + sqrt(2))^n. In the commutative ring Z[sqrt(2)], the set { +/ (1 + sqrt(2)^n} is a multiplicative group.  Michel Lagneau, Nov 27 2015


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,1).


FORMULA

a(n) = 2*a(n2) + a(n4) for n > 4.  R. J. Mathar, Feb 19 2009
G.f.: x*(1+x+x^2)/(12*x^2x^4).  Bruno Berselli, Mar 14 2012


MATHEMATICA

LinearRecurrence[{0, 2, 0, 1}, {1, 1, 3, 2}, 40] (* Vincenzo Librandi, Mar 14 2012 *)


PROG

(Haskell)
import Data.List (transpose)
a155046 n = a155046_list !! n
a155046_list = concat $ transpose [tail a001333_list, tail a000129_list]
 Reinhard Zumkeller, Jan 01 2014
(PARI) Vec(x*(1+x+x^2)/(12*x^2x^4) + O(x^50)) \\ Michel Marcus, Nov 28 2015


CROSSREFS

Cf. A002965.  Jaume Oliver Lafont, Feb 08 2009
Cf. A000129, A001333, A078057.
Sequence in context: A318783 A253564 A232751 * A236388 A033318 A093780
Adjacent sequences: A155043 A155044 A155045 * A155047 A155048 A155049


KEYWORD

nonn,easy,tabf


AUTHOR

Vincenzo Librandi, Jan 19 2009


EXTENSIONS

First term in two pairs corrected by R. J. Mathar, Feb 19 2009


STATUS

approved



