A158222 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A158222

a(n) = 196*n^2 + 2*n.

198, 788, 1770, 3144, 4910, 7068, 9618, 12560, 15894, 19620, 23738, 28248, 33150, 38444, 44130, 50208, 56678, 63540, 70794, 78440, 86478, 94908, 103730, 112944, 122550, 132548, 142938, 153720, 164894, 176460, 188418, 200768, 213510, 226644

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

The identity (196*n+1)^2-(196*n^2+2*n)*(14)^2=1 can be written as A158223(n)^2-a(n)*(14)^2=1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(14^2*t+2)).

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

G.f.: x*(-194*x-198)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {198, 788, 1770}, 50]

Table[196n^2+2n, {n, 50}] (* Harvey P. Dale, Jul 10 2021 *)

PROG

(Magma) I:=[198, 788, 1770]; [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) = 196*n^2+2*n.

CROSSREFS

Cf. A158223.