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A173089
a(n) = 25*n^2 + n.
3
26, 102, 228, 404, 630, 906, 1232, 1608, 2034, 2510, 3036, 3612, 4238, 4914, 5640, 6416, 7242, 8118, 9044, 10020, 11046, 12122, 13248, 14424, 15650, 16926, 18252, 19628, 21054, 22530, 24056, 25632, 27258, 28934, 30660, 32436, 34262, 36138, 38064, 40040, 42066, 44142, 46268, 48444, 50670, 52946, 55272, 57648
OFFSET
1,1
COMMENTS
The identity (5000*n^2 + 200*n + 1)^2 - (25*n^2 + n)*(1000*n + 20)^2 = 1 can be written as A157511(n)^2 - a(n)*A157510(n)^2 = 1. This is the case s=5 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, Feb 04 2012
FORMULA
G.f.: x*(-26 - 24*x)/(x-1)^3. - Vincenzo Librandi, Feb 04 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 04 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {26, 102, 228}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
Table[25n^2+n, {n, 50}] (* Harvey P. Dale, Sep 15 2024 *)
PROG
(Magma) [ 25*n^2+n: n in [1..50] ];
(PARI) for(n=1, 40, print1(25*n^2 + n", ")); \\ Vincenzo Librandi, Feb 04 2012
CROSSREFS
Sequence in context: A136293 A065013 A031434 * A333055 A244633 A042320
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Nov 22 2010
STATUS
approved