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A157369
a(n) = 343*n - 273.
3
70, 413, 756, 1099, 1442, 1785, 2128, 2471, 2814, 3157, 3500, 3843, 4186, 4529, 4872, 5215, 5558, 5901, 6244, 6587, 6930, 7273, 7616, 7959, 8302, 8645, 8988, 9331, 9674, 10017, 10360, 10703, 11046, 11389, 11732, 12075, 12418, 12761, 13104, 13447
OFFSET
1,1
COMMENTS
The identity (2401*n^2-3822*n+1520)^2-(49*n^2-78*n+31)*(343*n-273)^2=1 can be written as A157370(n)^2-A157368(n)*a(n)^2=1.
FORMULA
G.f: x*(70+273*x)/(1-x)^2.
E.g.f.: 7*(39 - (39-49*x)*exp(x)). - G. C. Greubel, Feb 02 2018
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {70, 413, 756}, 40]
343Range[40]-273 (* Harvey P. Dale, Mar 13 2011 *)
PROG
(Magma) I:=[70, 413, 756]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)= 343*n-273.
CROSSREFS
Sequence in context: A295770 A151556 A172222 * A163434 A154085 A220365
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 28 2009
STATUS
approved