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A157507
a(n) = 81*n^2 - 2*n.
3
79, 320, 723, 1288, 2015, 2904, 3955, 5168, 6543, 8080, 9779, 11640, 13663, 15848, 18195, 20704, 23375, 26208, 29203, 32360, 35679, 39160, 42803, 46608, 50575, 54704, 58995, 63448, 68063, 72840, 77779, 82880, 88143, 93568, 99155, 104904
OFFSET
1,1
COMMENTS
The identity (13122*n^2 - 324*n + 1)^2 - (81*n^2 - 2*n)*(1458*n - 18)^2 = 1 can be written as A157509(n)^2 - a(n)* A157508(n)^2 = 1 (see also second comment at A157509). - Vincenzo Librandi, Jan 26 2012
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jan 26 2012
G.f.: x*(-79 - 83*x)/(x-1)^3. - Vincenzo Librandi, Jan 26 2012
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {79, 320, 723}, 40] (* Vincenzo Librandi, Jan 26 2012 *)
Table[81n^2-2n, {n, 40}] (* Harvey P. Dale, Jun 10 2020 *)
PROG
(Magma) I:=[79, 320, 723]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jan 26 2012
(PARI) for(n=1, 22, print1(81*n^2 - 2*n", ")); \\ Vincenzo Librandi, Jan 26 2012
CROSSREFS
Sequence in context: A341182 A158769 A158774 * A142897 A142330 A007254
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 02 2009
STATUS
approved