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A156636
a(n) = 4394*n + 1820.
4
1820, 6214, 10608, 15002, 19396, 23790, 28184, 32578, 36972, 41366, 45760, 50154, 54548, 58942, 63336, 67730, 72124, 76518, 80912, 85306, 89700, 94094, 98488, 102882, 107276, 111670, 116064, 120458, 124852, 129246, 133640, 138034, 142428, 146822, 151216, 155610
OFFSET
0,1
COMMENTS
The identity (57122*n^2 + 47320*n + 9801)^2 - (169*n^2 + 140*n + 29)*(4394*n + 1820)^2 = 1 can be written as A156735(n)^2 - A156640(n)*a(n)^2 = 1.
FORMULA
G.f.: 26*(70+99*x)/(x-1)^2. - R. J. Mathar, Jan 05 2011
a(n) = 2*a(n-1) - a(n-2).
E.g.f.: 26*exp(x)*(70 + 169*x). - Elmo R. Oliveira, Dec 08 2024
MATHEMATICA
LinearRecurrence[{2, -1}, {1820, 6214}, 50]
PROG
(Magma) I:=[1820, 6214]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..50]];
(PARI) a(n)=4394*n+1820 \\ Charles R Greathouse IV, Dec 23 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Feb 15 2009
EXTENSIONS
Offset corrected by R. J. Mathar, Jan 05 2011
STATUS
approved