OFFSET
0,3
COMMENTS
LINKS
Reinhard Zumkeller, Rows n = 0..125 of triangle, flattened
H. Fuks and J.M.G. Soto, Exponential convergence to equilibrium in cellular automata asymptotically emulating identity, arXiv:1306.1189 [nlin.CG], 2013.
FORMULA
EXAMPLE
Triangle begins:
1;
0, 2;
0, 1, 3;
0, 0, 3, 5;
0, 0, 1, 7, 8;
0, 0, 0, 4, 15, 13;
0, 0, 0, 1, 12, 30, 21;
0, 0, 0, 0, 5, 31, 58, 34;
MATHEMATICA
T[n_, k_]:= If[k<0 || k>n, 0, If[n==0 && k==0, 1, If[k==0, 0, If[n==1 && k==1, 2, T[n-1, k-1] + T[n-2, k-1] + T[n-2, k-2]]]]]; Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, May 21 2019 *)
PROG
(Haskell)
a236076 n k = a236076_tabl !! n !! k
a236076_row n = a236076_tabl !! n
a236076_tabl = [1] : [0, 2] : f [1] [0, 2] where
f us vs = ws : f vs ws where
ws = [0] ++ zipWith (+) (zipWith (+) ([0] ++ us) (us ++ [0])) vs
-- Reinhard Zumkeller, Jan 19 2014
(PARI)
{T(n, k) = if(k<0 || k>n, 0, if(n==0 && k==0, 1, if(k==0, 0, if(n==1 && k==1, 2, T(n-1, k-1) + T(n-2, k-1) + T(n-2, k-2) ))))}; \\ G. C. Greubel, May 21 2019
(Sage)
def T(n, k):
if (k<0 or k>n): return 0
elif (n==0 and k==0): return 1
elif (k==0): return 0
elif (n==1 and k==1): return 2
else: return T(n-1, k-1) + T(n-2, k-1) + T(n-2, k-2)
[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, May 21 2019
CROSSREFS
KEYWORD
AUTHOR
Philippe Deléham, Jan 19 2014
STATUS
approved