OFFSET
0,4
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
Tian-Xiao He and Renzo Sprugnoli, Sequence characterization of Riordan arrays, Discrete Math. 309 (2009), no. 12, 3962-3974. [N. J. A. Sloane, Nov 26 2011]
FORMULA
Riordan array (1/(1-x-x^2), xc(x)), c(x) the g.f. of A000108.
T(n,k) = k * Sum_{i=0..n-k} (Fibonacci(i+1)*binomial(2*(n-i)-k-1,n-i-1)/(n-i)) if k>0, and Fibonacci(n+1) if k=0. - Vladimir Kruchinin, Mar 09 2011
EXAMPLE
Triangle begins
1,
1, 1,
2, 2, 1,
3, 5, 3, 1,
5, 12, 9, 4, 1,
8, 31, 26, 14, 5, 1,
13, 85, 77, 46, 20, 6, 1,
21, 248, 235, 150, 73, 27, 7, 1,
34, 762, 741, 493, 258, 108, 35, 8, 1
The production matrix for this array is
1, 1,
1, 1, 1,
-1, 1, 1, 1,
0, 1, 1, 1, 1,
0, 1, 1, 1, 1, 1,
0, 1, 1, 1, 1, 1, 1,
0, 1, 1, 1, 1, 1, 1
MAPLE
RIORDAN := proc(d, h, n, k)
d*h^k ;
expand(%) ;
coeftayl(%, x=0, n) ;
end proc:
A139375 := proc(n, k)
RIORDAN(1/(1-x-x^2), (1-sqrt(1-4*x))/2, n, k) ;
end proc: # R. J. Mathar, Jul 09 2013
MATHEMATICA
T[n_, 0]:= Fibonacci[n + 1]; T[n_, k_]:= k*Sum[Fibonacci[i + 1]*Binomial[2*(n - i) - k - 1, n - i - 1]/(n - i), {i, 0, n - k}]; Table[T[n, k], {n, 0, 49}, {k, 0, n}] // Flatten (* G. C. Greubel, Oct 20 2016 *)
CROSSREFS
KEYWORD
AUTHOR
Paul Barry, Apr 15 2008
EXTENSIONS
Alternative name added by N. J. A. Sloane, Nov 27 2011
STATUS
approved