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A157330
a(n) = 64*n - 8.
2
56, 120, 184, 248, 312, 376, 440, 504, 568, 632, 696, 760, 824, 888, 952, 1016, 1080, 1144, 1208, 1272, 1336, 1400, 1464, 1528, 1592, 1656, 1720, 1784, 1848, 1912, 1976, 2040, 2104, 2168, 2232, 2296, 2360, 2424, 2488, 2552, 2616, 2680, 2744, 2808, 2872
OFFSET
1,1
COMMENTS
The identity (128*n^2 - 32*n + 1)^2 - (4*n^2 - n)*(64*n - 8)^2 = 1 can be written as A157331(n)^2 - A033991(n)*a(n)^2 = 1. This is the case s=2 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. - Vincenzo Librandi, Jan 29 2012
FORMULA
From Vincenzo Librandi, Jan 29 2012: (Start)
a(n) = 2*a(n-1) - a(n-2).
G.f.: x*(8*x+56)/(x-1)^2. (End)
a(n) = 8*A004771(n-1). - Michel Marcus, Aug 19 2018
MATHEMATICA
LinearRecurrence[{2, -1}, {56, 120}, 50] (* Vincenzo Librandi, Jan 29 2012 *)
PROG
(Magma) I:=[56, 120]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
(PARI) for(n=1, 40, print1(64*n - 8", ")); \\ Vincenzo Librandi, Jan 29 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 27 2009
STATUS
approved