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A111365 a(n) = 5*a(n-1) + 3*a(n-2) where a(0) = a(1) = 1. 0
1, 1, 8, 43, 239, 1324, 7337, 40657, 225296, 1248451, 6918143, 38336068, 212434769, 1177182049, 6523214552, 36147618907, 200307738191, 1109981547676, 6150830952953, 34084099407793, 188872989897824, 1046617247712499 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001

LINKS

Table of n, a(n) for n=0..21.

Index entries for linear recurrences with constant coefficients, signature (5, 3).

FORMULA

a(n)=(1/2)*[5/2-(1/2)*sqrt(37)]^n-(3/74)*[5/2+(1/2)*sqrt(37)]^n*sqrt(37)+(3/74)*[5/2-(1/2) *sqrt(37)]^n*sqrt(37)+(1/2)*[5/2+(1/2)*sqrt(37)]^n, with n>=0 [From Paolo P. Lava, Aug 01 2008]

a(n)=A015536(n+1)-4*A015536(n). G.f.: (1-4x)/(1-5x-3x^2). [From R. J. Mathar, Jul 08 2009]

EXAMPLE

a(2) = 5*a(1) + 3*a(0) = 5*1 + 3*1 = 8 which is the third term in the sequence.

MATHEMATICA

Transpose[NestList[Flatten[{Rest[#], ListCorrelate[{3, 5}, #]}]&, {1, 1}, 40]][[1]]  (* Harvey P. Dale, Mar 23 2011 *)

CROSSREFS

Cf. A000045, A072264.

Sequence in context: A239033 A034361 A117617 * A199321 A144039 A282189

Adjacent sequences:  A111362 A111363 A111364 * A111366 A111367 A111368

KEYWORD

nonn

AUTHOR

Parthasarathy Nambi, Nov 07 2005

EXTENSIONS

More terms from Robert G. Wilson v, Nov 10 2005

STATUS

approved

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Last modified May 15 01:50 EDT 2021. Contains 343909 sequences. (Running on oeis4.)