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A049680 a(n) = (L(n) + L(2*n))/2, where L = A000032 (the Lucas sequence). 2
2, 2, 5, 11, 27, 67, 170, 436, 1127, 2927, 7625, 19901, 52002, 135982, 355745, 930931, 2436527, 6377807, 16695530, 43706576, 114420627, 299549527, 784218605, 2053091161, 5375030402, 14071960442, 36840786845, 96450296411 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..2388

Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).

FORMULA

Binomial transform of trace(A^n)/4, where A is the adjacency matrix of path graph P_4 (A005248 with interpolated zeros). - Paul Barry, Apr 24 2004

From George F. Johnson, Feb 04 2013: (Start)

G.f.: (1-x)*(2-4*x-x^2)/ ( (1-x-x^2)*(1-3*x+x^2) ).

a(n) = 4*a(n-1) - 3*a(n-2) - 2*a(n-3) + a(n-4) for n>3. (End)

EXAMPLE

a(8) = (L(8) + L(2 * 8)) / 2 = (47 + 2207) / 2 = 2254 / 2 = 1127. - Indranil Ghosh, Feb 06 2017

MATHEMATICA

LinearRecurrence[{4, -3, -2, 1}, {2, 2, 5, 11}, 30] (* Harvey P. Dale, Nov 22 2015 *)

Table[(LuasL[n] + LucasL[2*n])/2, {n, 0, 30}] (* G. C. Greubel, Dec 02 2017 *)

PROG

(PARI) x='x+O('x^30); Vec((1-x)*(2-4*x-x^2)/ ( (1-x-x^2)*(1-3*x+x^2) )) \\ G. C. Greubel, Dec 02 2017

(MAGMA) [(Lucas(n) + Lucas(2*n)/2: n in [0..30]]; // G. C. Greubel, Dec 02 2017

CROSSREFS

Sequence in context: A112527 A216642 A227999 * A153983 A262714 A058021

Adjacent sequences:  A049677 A049678 A049679 * A049681 A049682 A049683

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified April 25 16:08 EDT 2019. Contains 322461 sequences. (Running on oeis4.)