A133678 a(n)=6*a(n-1)+42*a(n-2) for n>=3, a(0)=1, a(1)=6, a(2)=72 .

1, 6, 72, 684, 7128, 71496, 728352, 7372944, 74828448, 758634336, 7694600832, 78030247104, 791354717568, 8025398683776, 81389290240512, 825402486161664, 8370765107071488, 84891495061218816, 860921104864315392, 8730969421757082624, 88544502934843742208

Offset: 0

Author

Philippe Deléham, Dec 31 2007

Keywords

• easy
• nonn

References

• D. A. Cox, Primes of the form x^2+ny^2, Wiley, New York, 1989.
• D. E. Flath, Introduction to Number Theory, Wiley-Interscience, 1989.

Links

• Index entries for linear recurrences with constant coefficients, signature (6,42).

Programs

Mathematica

Join[{1},LinearRecurrence[{6,42},{6,72},20]] (* Harvey P. Dale, Mar 25 2015 *)

Formula

G.f.: (1-6*x^2)/(1-6*x-42*x^2) . a(n) = Sum_{k, 0<=k<=n}A122950(n,k)*6^k .

a(1)=6, a(2)=72, a(n)=6*a(n-1)+42*a (n-2). - Harvey P. Dale, Mar 25 2015

Extensions

Corrected and extended by Harvey P. Dale, Mar 25 2015