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A027978 a(n) = self-convolution of row n of array T given by A027960. 1
1, 11, 42, 145, 473, 1484, 4529, 13543, 39870, 115937, 333781, 953056, 2702497, 7618115, 21365778, 59657329, 165926609, 459905588, 1270819025, 3501855007, 9625627686, 26398369601, 72248624077, 197361589960, 538199264833 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1).

FORMULA

From Colin Barker, Feb 25 2015: (Start)

a(n) = 5*a(n-1) - 5*a(n-2) - 5*a(n-3) + 5*a(n-4) - a(n-5).

G.f.: (1 +5*x -13*x^2 +8*x^3)/(1-3*x+x^2)^2. (End)

a(n) = 2*(n+1)*Lucas(2*n) + Fibonacci(2*n-4). - G. C. Greubel, Oct 01 2019

MAPLE

with(combinat); f:=fibonacci; seq(2*(n+1)*(f(2*n+1) + f(2*n-1)) + f(2*n-4), n=0..40); # G. C. Greubel, Oct 01 2019

MATHEMATICA

Table[2*(n+1)*LucasL[2*n] + Fibonacci[2*n-4], {n, 0, 40}] (* G. C. Greubel, Oct 01 2019 *)

PROG

(PARI) vector(41, n, f=fibonacci; 2*n*(f(2*n-1) + f(2*n-3)) + f(2*n-6)) \\ G. C. Greubel, Oct 01 2019

(MAGMA) [2*(n+1)*Lucas(2*n) + Fibonacci(2*n-4): n in [0..40]]; // G. C. Greubel, Oct 01 2019

(Sage) [2*(n+1)*lucas_number2(2*n, 1, -1) + fibonacci(2*n-4) for n in (0..40)] # G. C. Greubel, Oct 01 2019

(GAP) List([0..40], n-> 2*(n+1)*Lucas(1, -1, 2*n)[2] + Fibonacci(2*n-4) ); # G. C. Greubel, Oct 01 2019

CROSSREFS

Cf. A000032, A000045, A027960.

Sequence in context: A055436 A213772 A062517 * A050489 A156533 A228811

Adjacent sequences:  A027975 A027976 A027977 * A027979 A027980 A027981

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)