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

Author

Clark Kimberling

Keywords

• nonn

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).

Crossrefs

Cf. A000032, A000045, A027960.

Programs

GAP

List([0..40], n-> 2*(n+1)*Lucas(1,-1,2*n)[2] + Fibonacci(2*n-4) ); # 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

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 *)

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

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

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