A053430 a(n) = (6^(n+1) - (-5)^(n+1))/11.

1, 1, 31, 61, 991, 2821, 32551, 117181, 1093711, 4609141, 37420471, 175694701, 1298308831, 6569149861, 45518414791, 242592910621, 1608145354351, 8885932672981, 57130293303511, 323708273492941, 2037617072598271

Offset

0,3

Comments

Hankel transform is := 1,30,0,0,0,0,0,0,0,0,0,0,... - Philippe Deléham, Nov 02 2008

The ratio a(n+1)/a(n) converges to 6 as n approaches infinity. - Felix P. Muga II, Mar 10 2014

References

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

F. P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, March 2014; Preprint on ResearchGate.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. K. Whitford, Binet's Formula Generalized, Fibonacci Quarterly, Vol. 15, No. 1, 1979, pp. 21, 24, 29.

Index entries for linear recurrences with constant coefficients, signature (1,30).

Formula

G.f.: -1/(5*x+1)/(6*x-1). - R. J. Mathar, Nov 16 2007

a(0)=1, a(1)=1, a(n) = a(n-1) + 30*a(n-2). - Harvey P. Dale, May 09 2012

Maple

A053430:=n->( 6^(n+1)-(-5)^(n+1) )/11; seq(A053430(n), n=0..20); # Wesley Ivan Hurt, Mar 11 2014

Mathematica

Join[{a=1, b=1}, Table[c=b+30*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 01 2011 *)
Table[(6^(n+1)-(-5)^(n+1))/11, {n, 0, 20}] (* Harvey P. Dale, May 09 2012 *)
LinearRecurrence[{1, 30}, {1, 1}, 21] (* Harvey P. Dale, May 09 2012 *)
CoefficientList[Series[-1/(5 x + 1)/(6 x - 1), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 11 2014 *)

Prog

(PARI) a(n) = ( 6^(n+1)-(-5)^(n+1) )/11; \\ Joerg Arndt, Mar 10 2014
(Magma) [(6^(n+1)-(-5)^(n+1))/11: n in [0..30]]; // Vincenzo Librandi, Mar 11 2014

Crossrefs

Cf. A001045, A015441, A053404.

Sequence in context: A088463 A195745 A078855 * A040930 A115809 A303698

Adjacent sequences: A053427 A053428 A053429 * A053431 A053432 A053433

Keyword

easy,nonn

Author

Barry E. Williams, Jan 10 2000

Extensions

More terms from James A. Sellers, Feb 02 2000

Status

approved