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A157446 a(n) = 16*n^2 - n. 4
15, 62, 141, 252, 395, 570, 777, 1016, 1287, 1590, 1925, 2292, 2691, 3122, 3585, 4080, 4607, 5166, 5757, 6380, 7035, 7722, 8441, 9192, 9975, 10790, 11637, 12516, 13427, 14370, 15345, 16352, 17391, 18462, 19565, 20700, 21867, 23066, 24297, 25560 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The identity (2048*n^2 - 128*n + 1)^2 - (16*n^2 - n)*(512*n - 16)^2 = 1 can be written as A157448(n)^2 - a(n)*A157447(n)^2 = 1. - Vincenzo Librandi, Jan 26 2012
This is the case s=4 of the identity (8*n^2*s^4 - 8*n*s^2 + 1)^2 - (n^2*s^2 - n)*(8*n*s^3 - 4*s)^2 = 1. - Bruno Berselli, Jan 26 2012
Sequence found by reading the line from 15, in the direction 15, 62, ... in the square spiral whose vertices are the generalized decagonal numbers A074377. - Omar E. Pol, Nov 02 2012
The continued fraction expansion of sqrt(a(n)) is [4n-1; {1, 6, 1, 8n-2}]. For n=1, this collapses to [3; {1, 6}]. - Magus K. Chu, Sep 22 2022
LINKS
Vincenzo Librandi, X^2-AY^2=1
FORMULA
G.f.: x*(15 + 17*x)/(1-x)^3. - Vincenzo Librandi, Jan 26 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {15, 62, 141}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
PROG
(Magma) I:=[15, 62, 141]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 22, print1(16*n^2 - n", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
Sequence in context: A072201 A218811 A219819 * A220084 A240711 A212055
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 01 2009
STATUS
approved

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Last modified March 18 22:09 EDT 2024. Contains 370951 sequences. (Running on oeis4.)