OFFSET
0,5
COMMENTS
Deleting the right border gives triangle A117895.
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
Rows are composed of difference terms of triangle A117584.
Rows sum to Pell numbers, A000129.
From G. C. Greubel, Sep 27 2021: (Start)
T(n, 1) = n for n >= 1.
T(n, 2) = n for n >= 2.
T(n, n) = [n=0] + A000129(n).
T(n, n-1) = 2*[n=0] + A078343(n). (End)
EXAMPLE
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==0, 1, (k-n)*Fibonacci[k+1, 2] + (3*n-3*k+1)*Fibonacci[k, 2]]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* G. C. Greubel, Sep 27 2021 *)
PROG
(Magma) Pell:= func< n | Round(((1+Sqrt(2))^n - (1-Sqrt(2))^n)/(2*Sqrt(2))) >;
[k eq 0 select 1 else (k-n)*Pell(k+1) + (3*n-3*k+1)*Pell(k): k in [0..n], n in [0..12]]; // G. C. Greubel, Sep 27 2021
(Sage)
def P(n): return lucas_number1(n, 2, -1)
def A117894(n, k): return 1 if (k==0) else (k-n)*P(k+1) + (3*n-3*k+1)*P(k)
flatten([[A117894(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Sep 27 2021
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 30 2006
STATUS
approved