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A158550
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a(n) = 169*n^2 - 13.
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2
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156, 663, 1508, 2691, 4212, 6071, 8268, 10803, 13676, 16887, 20436, 24323, 28548, 33111, 38012, 43251, 48828, 54743, 60996, 67587, 74516, 81783, 89388, 97331, 105612, 114231, 123188, 132483, 142116, 152087, 162396, 173043, 184028, 195351
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OFFSET
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1,1
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COMMENTS
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The identity (26*n^2 - 1)^2 - (169*n^2 - 13)*(2*n)^2 = 1 can be written as A158551(n)^2 - a(n)*A005843(n)^2 = 1.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: 13*x*(-12 - 15*x + x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {156, 663, 1508}, 40] (* Vincenzo Librandi, Feb 14 2012 *)
169*Range[40]^2-13 (* Harvey P. Dale, Apr 12 2017 *)
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PROG
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(MAGMA) I:=[156, 663, 1508]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 14 2012
(PARI) for(n=1, 40, print1(169*n^2 - 13", ")); \\ Vincenzo Librandi, Feb 14 2012
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CROSSREFS
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Cf. A005843, A158551.
Sequence in context: A259947 A043356 A038476 * A156994 A304619 A204718
Adjacent sequences: A158547 A158548 A158549 * A158551 A158552 A158553
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 21 2009
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EXTENSIONS
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Comment rewritten by R. J. Mathar, Oct 16 2009
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STATUS
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approved
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