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A007572 Generalization of the golden ratio (expansion of (5-13x)/((1+x)(1-4x))).
(Formerly M3735)
1
5, 2, 26, 86, 362, 1430, 5738, 22934, 91754, 366998, 1468010, 5872022, 23488106, 93952406, 375809642, 1503238550, 6012954218, 24051816854, 96207267434, 384829069718, 1539316278890, 6157265115542, 24629060462186 (list; graph; refs; listen; history; text; internal format)
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 A224494 A095998

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

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Last modified October 18 03:51 EDT 2018. Contains 316304 sequences. (Running on oeis4.)