A093117 a(n) = 8*a(n-1) + 21*a(n-2), with a(1)=1, a(2)=15.

1, 15, 141, 1443, 14505, 146343, 1475349, 14875995, 149990289, 1512318207, 15248341725, 153745416147, 1550178505401, 15630081782295, 157594402871781, 1588986940402443, 16021377983526945, 161539749616666863, 1628766934587400749, 16422470218649210115

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..990

Index entries for linear recurrences with constant coefficients, signature (8,21).

Formula

Limit_{n -> oo} a(n+1)/a(n) converges to 4 + sqrt(37).

G.f.: x*(1+7*x)/(1-8*x-21*x^2). - Stefan Steinerberger, Nov 18 2005

a(n) = A093103(n) + 7*A093103(n-1). - G. C. Greubel, Feb 10 2023

Mathematica

LinearRecurrence[{8, 21}, {1, 15}, 20] (* Harvey P. Dale, Nov 03 2020 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+7*x)/(1-8*x-21*x^2) )); // G. C. Greubel, Feb 09 2023
(SageMath)
@CachedFunction
def b(n): # b = A093103
    if (n<3): return (0, 1, 8)[n]
    else: return 8*b(n-1) + 21*b(n-2)
def A093117(n): return b(n) + 7*b(n-1)
[A093117(n) for n in range(1, 41)] # G. C. Greubel, Feb 09 2023

Crossrefs

Cf. A093103, A094703.

Sequence in context: A320818 A026859 A096046 * A045724 A241402 A252825

Adjacent sequences: A093114 A093115 A093116 * A093118 A093119 A093120

Keyword

nonn,easy

Author

Gary W. Adamson, May 21 2004

Extensions

More terms from Robert G. Wilson v, May 24 2004

Edited by Don Reble, Nov 04 2005

Status

approved