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A154375
a(n) = 1250*n^2 + 100*n + 1.
3
1351, 5201, 11551, 20401, 31751, 45601, 61951, 80801, 102151, 126001, 152351, 181201, 212551, 246401, 282751, 321601, 362951, 406801, 453151, 502001, 553351, 607201, 663551, 722401, 783751, 847601, 913951, 982801, 1054151, 1128001
OFFSET
1,1
COMMENTS
The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as a(n)^2 - A154377(n)*A154379(n)^2 = 1. - Vincenzo Librandi, Jan 30 2012
This is the case s=5 of the identity (2*s^4*n^2 + 4*s^2*n + 1)^2 - (s^2*n^2 + 2*n)*(2*s^3*n + 2*s)^2 = 1. - Bruno Berselli, Jan 30 2012
FORMULA
a(1)=1351, a(2)=5201, a(3)=11551, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Apr 25 2011
G.f.: x*(x^2 + 1148*x + 1351)/(1-x)^3. - Vincenzo Librandi, Jan 30 2012
E.g.f.: (1250*x^2 + 1350*x + 1)*exp(x) - 1. - G. C. Greubel, Sep 15 2016
MATHEMATICA
Table[1250n^2+100n+1, {n, 30}] (* or *) LinearRecurrence[{3, -3, 1}, {1351, 5201, 11551}, 30] (* Harvey P. Dale, Apr 25 2011 *)
PROG
(PARI) a(n)=1250*n^2+100*n+1 \\ Charles R Greathouse IV, Dec 27 2011
CROSSREFS
Sequence in context: A307218 A278383 A174638 * A243132 A349070 A035889
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Jan 08 2009
EXTENSIONS
Minor corrections by M. F. Hasler, Oct 08 2014
STATUS
approved