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A157105
a(n) = 137842*n - 30996.
4
106846, 244688, 382530, 520372, 658214, 796056, 933898, 1071740, 1209582, 1347424, 1485266, 1623108, 1760950, 1898792, 2036634, 2174476, 2312318, 2450160, 2588002, 2725844, 2863686, 3001528, 3139370, 3277212, 3415054
OFFSET
1,1
COMMENTS
The identity (5651522*n^2 - 2541672*n + 285769)^2 - (1681*n^2 - 756*n + 85)*(137842*n - 30996)^2 = 1 can be written as (A157106(n))^2 - (A157010(n))*(a(n))^2 = 1.
FORMULA
a(n) = 2*a(n-1) -a(n-2).
G.f: 82*x*(1303 + 378*x)/(1-x)^2.
E.g.f.: 82*(378 - (378 - 1681*x)*exp(x)). - G. C. Greubel, Jan 11 2022
MATHEMATICA
LinearRecurrence[{2, -1}, {106846, 244688}, 30] (* Harvey P. Dale, Mar 31 2013 *)
82*(1681*Range[30] -378) (* G. C. Greubel, Jan 11 2022 *)
PROG
(Magma) I:=[106846, 244688, 382530]; [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) = 137842*n - 30996
(Sage) [82*(1681*n - 378) for n in (1..30)] # G. C. Greubel, Jan 11 2022
CROSSREFS
Sequence in context: A253404 A223343 A028466 * A122711 A297994 A237216
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 23 2009
STATUS
approved