



13, 49, 109, 193, 301, 433, 589, 769, 973, 1201, 1453, 1729, 2029, 2353, 2701, 3073, 3469, 3889, 4333, 4801, 5293, 5809, 6349, 6913, 7501, 8113, 8749, 9409, 10093, 10801, 11533, 12289, 13069, 13873, 14701, 15553, 16429, 17329, 18253, 19201
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OFFSET

1,1


COMMENTS

The identity (12*n^2+1)^2  (36*n^2+6)*(2*n)^2 = 1 can be written as a(n)^2  A158479(n)*A005843(n)^2 = 1.
Sequence found by reading the line from 13, in the direction 13, 49, ..., in the square spiral whose vertices are the generalized octagonal numbers A001082.  Omar E. Pol, Jul 18 2012


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vincenzo Librandi, X^2AY^2=1
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

a(n) = A010014(n)/2.  Vladimir Joseph Stephan Orlovsky, May 18 2009
G.f: x*(13+10*x+x^2)/(1x)^3.
a(n) = 3*a(n1) 3*a(n2) +a(n3).
a(n) = 1 + A135453(n).  Omar E. Pol, Jul 18 2012


EXAMPLE

For n=1, a(1)=13; n=2, a(2)=49; n=3, a(3)=109.


MATHEMATICA

a=1; lst={}; Do[b=n^3a; AppendTo[lst, b/2]; a+=b, {n, 3, 6!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, May 18 2009 *)
LinearRecurrence[{3, 3, 1}, {13, 49, 109}, 40]


PROG

(MAGMA) I:=[13, 49, 109]; [n le 3 select I[n] else 3*Self(n1)3*Self(n2)+Self(n3): n in [1..50]];
(PARI) a(n)=12*n^2+1


CROSSREFS

Cf. A005843, A158479.
Sequence in context: A305480 A044115 A044496 * A009951 A274974 A251142
Adjacent sequences: A158477 A158478 A158479 * A158481 A158482 A158483


KEYWORD

nonn,easy


AUTHOR

Vincenzo Librandi, Mar 20 2009


STATUS

approved



