A027978 a(n) = self-convolution of row n of array T given by A027960.

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

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