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A157436
a(n) = 128*n^2 + 2528*n + 12481.
3
15137, 18049, 21217, 24641, 28321, 32257, 36449, 40897, 45601, 50561, 55777, 61249, 66977, 72961, 79201, 85697, 92449, 99457, 106721, 114241, 122017, 130049, 138337, 146881, 155681, 164737, 174049, 183617, 193441, 203521, 213857, 224449
OFFSET
1,1
COMMENTS
The identity (128*n^2 + 2528*n + 12481)^2 - (4*n^2 + 79*n + 390)*(64*n + 632)^2 = 1 can be written as a(n)^2 - A157434(n)* A157435(n)^2 = 1.
FORMULA
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
G.f.: x*(-12481*x^2 + 27362*x - 15137)/(x-1)^3. [corrected by Georg Fischer, May 11 2019]
MATHEMATICA
LinearRecurrence[{3, -3, 1}, {15137, 18049, 21217}, 50]
PROG
(Magma) I:=[15137, 18049, 21217]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];
(PARI) a(n) = 128*n^2 + 2528*n + 12481.
CROSSREFS
Sequence in context: A004935 A004955 A004975 * A196495 A031623 A105924
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Mar 01 2009
EXTENSIONS
Corrected by Charles R Greathouse IV, Jul 29 2010
STATUS
approved