A157362 a(n) = 49*n^2 - 2*n.

47, 192, 435, 776, 1215, 1752, 2387, 3120, 3951, 4880, 5907, 7032, 8255, 9576, 10995, 12512, 14127, 15840, 17651, 19560, 21567, 23672, 25875, 28176, 30575, 33072, 35667, 38360, 41151, 44040, 47027, 50112, 53295, 56576, 59955, 63432, 67007

Offset: 1

Author

Vincenzo Librandi, Feb 28 2009

Keywords

• nonn
• easy

Comments

The identity (4802*n^2-196*n+1)^2-(49*n^2-2*n)*(686*n-14)^2=1 can be written as A157364(n)^2-a(n)*A157363(n)^2=1.

The continued fraction expansion of sqrt(4*a(n)) is [14n-1; {1, 2, 2, 7n-1, 2, 2, 1, 28n-2}]. - Magus K. Chu, Sep 17 2022

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A157363, A157364.

Programs

Magma

I:=[47, 192, 435]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];

Mathematica

LinearRecurrence[{3,-3,1},{47,192,435},50]
Table[49n^2-2n,{n,40}] (* Harvey P. Dale, Jun 10 2019 *)

PARI

a(n)=49*n^2-2*n \\ Charles R Greathouse IV, Dec 23 2011

Formula

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).

G.f.: x*(47+51*x)/(1-x)^3.

E.g.f. x*(47 + 49*x)*exp(x). - G. C. Greubel, Feb 02 2018