A108100 a(n) = (2*n-1)^2 + (2*n+1)^2.
2, 10, 34, 74, 130, 202, 290, 394, 514, 650, 802, 970, 1154, 1354, 1570, 1802, 2050, 2314, 2594, 2890, 3202, 3530, 3874, 4234, 4610, 5002, 5410, 5834, 6274, 6730, 7202, 7690, 8194, 8714, 9250, 9802, 10370, 10954, 11554, 12170, 12802, 13450, 14114, 14794, 15490
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
[8*n^2+2: n in [0..50]]; // Vincenzo Librandi, Sep 06 2011
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Mathematica
Table[8n^2+2,{n,0,50}] (* Harvey P. Dale, Feb 20 2011 *) -
Maxima
makelist(8*n^2+2,n,0,30); /* Martin Ettl, Nov 12 2012 */
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PARI
a(n)=(2*n-1)^2+(2*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017
Formula
From R. J. Mathar, Aug 24 2008: (Start)
O.g.f.: 2*(1 + 2*x + 5*x^2)/(1-x)^3.
a(n) = 2*A053755(n). (End)
a(n) = a(-n); a(n) + a(-n) = A158444(n). - Bruno Berselli, Sep 06 2011
a(n) = 2*(A000466(n) + 2). - Martin Ettl, Nov 12 2012
From Elmo R. Oliveira, Nov 16 2024: (Start)
E.g.f.: 2*exp(x)*(1 + 4*x + 4*x^2).
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)