OFFSET
1,2
COMMENTS
As T is also the triangle of sums of consecutive distinct Fibonacci numbers, a(n) is such a sum, namely Sum_{j=n+1..2n} Fibonacci(j).
LINKS
Muniru A Asiru, Table of n, a(n) for n = 1..2000
Index entries for linear recurrences with constant coefficients, signature (4,-3,-2,1).
FORMULA
a(n) = Fibonacci(2n+2) - Fibonacci(n+2) = A094585(2n-1, n).
G.f.: x*(1+x-x^2)/((1-x-x^2)*(1-3*x+x^2)). - Colin Barker, Sep 16 2012
EXAMPLE
a(4) = F(10)-F(6) = 55-8 = 47.
MATHEMATICA
Table[Sum[Fibonacci[n+i], {i, n}], {n, 30}] (* Zerinvary Lajos, Jul 12 2009 *)
With[{F=Fibonacci}, Table[F[2n+2]-F[n+2], {n, 30}]] (* G. C. Greubel, Jul 14 2019 *)
PROG
(GAP) List([1..30], n->Fibonacci(2*n+2)-Fibonacci(n+2)); # Muniru A Asiru, Apr 28 2019
(PARI) vector(30, n, f=fibonacci; f(2*n+2)-f(n+2)) \\ G. C. Greubel, Jul 14 2019
(Magma) F:=Fibonacci; [F(2*n+2)-F(n+2): n in [1..30]]; // G. C. Greubel, Jul 14 2019
(Sage) f=fibonacci; [f(2*n+2)-f(n+2) for n in (1..30)] # G. C. Greubel, Jul 14 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 13 2004
STATUS
approved