A007572 Generalization of the golden ratio (expansion of (5-13x)/((1+x)(1-4x))). (Formerly M3735)

5, 2, 26, 86, 362, 1430, 5738, 22934, 91754, 366998, 1468010, 5872022, 23488106, 93952406, 375809642, 1503238550, 6012954218, 24051816854, 96207267434, 384829069718, 1539316278890, 6157265115542, 24629060462186

Offset

0,1

References

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

A. K. Whitford, A generalization of the golden ratio, J. Rec. Math., 8 (No. 3, 1975-1976), 203-207.

Links

Table of n, a(n) for n=0..22.

A. K. Whitford, A generalization of the golden ratio, J. Rec. Math., 8 (No. 3, 1975-1976), 203-207. (Annotated scanned copy)

Index entries for linear recurrences with constant coefficients, signature (3, 4).

Formula

a(0)=5, a(1)=2, a(n)=3*a(n-1)+4*a(n-2). [Harvey P. Dale, Apr 15 2012]

Mathematica

CoefficientList[Series[(5-13x)/((1+x)(1-4x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 4}, {5, 2}, 30] (* Harvey P. Dale, Apr 15 2012 *)

Crossrefs

Sequence in context: A202141 A100080 A117734 * A297812 A360546 A347379

Adjacent sequences: A007569 A007570 A007571 * A007573 A007574 A007575

Keyword

nonn

Author

Simon Plouffe and N. J. A. Sloane, Robert G. Wilson v

Extensions

Clarified definition by Harvey P. Dale, Apr 15 2012

Status

approved