A157331 a(n) = 128*n^2 - 32*n + 1.
97, 449, 1057, 1921, 3041, 4417, 6049, 7937, 10081, 12481, 15137, 18049, 21217, 24641, 28321, 32257, 36449, 40897, 45601, 50561, 55777, 61249, 66977, 72961, 79201, 85697, 92449, 99457, 106721, 114241, 122017, 130049, 138337, 146881, 155681, 164737, 174049, 183617
Offset: 1
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..10000
- Vincenzo Librandi, X^2-AY^2=1
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
I:=[97, 449, 1057]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Jan 29 2012
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Mathematica
LinearRecurrence[{3,-3,1},{97,449,1057},40] (* Vincenzo Librandi, Jan 29 2012 *) -
PARI
for(n=1, 40, print1(128*n^2 - 32*n + 1", ")); \\ Vincenzo Librandi, Jan 29 2012
Formula
From Vincenzo Librandi, Jan 29 2012: (Start)
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(-97 - 158*x - x^2)/(x-1)^3. (End)
E.g.f.: exp(x)*(128*x^2 + 96*x + 1) - 1. - Stefano Spezia, May 02 2024
Comments