A156635 - OEIS

A156635

144*n^2 - n.

143, 574, 1293, 2300, 3595, 5178, 7049, 9208, 11655, 14390, 17413, 20724, 24323, 28210, 32385, 36848, 41599, 46638, 51965, 57580, 63483, 69674, 76153, 82920, 89975, 97318, 104949, 112868, 121075, 129570, 138353, 147424, 156783, 166430

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OFFSET

1,1

COMMENTS

The identity (288*n-1)^2-(144*n^2-n)*(24)^2=1 can be written as A157997(n)^2-a(n)*(24)^2=1.

LINKS

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(12^2*t-1)).

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*(-143-145*x)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {143, 574, 1293}, 50]

PROG

(Magma) I:=[143, 574, 1293]; [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)=144*n^2-n \\ Charles R Greathouse IV, Dec 23 2011

CROSSREFS

Cf. A157997.

Sequence in context: A126703 A111185 A074301 * A354483 A035304 A241924