A152719 Triangle read by rows: T(n,k) = A000129( 1 + min(k,n-k) ), n>=0, 0<=k<=n.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 5, 2, 1, 1, 2, 5, 5, 2, 1, 1, 2, 5, 12, 5, 2, 1, 1, 2, 5, 12, 12, 5, 2, 1, 1, 2, 5, 12, 29, 12, 5, 2, 1, 1, 2, 5, 12, 29, 29, 12, 5, 2, 1, 1, 2, 5, 12, 29, 70, 29, 12, 5, 2, 1, 1, 2, 5, 12, 29, 70, 70, 29, 12, 5, 2, 1, 1, 2, 5, 12, 29, 70, 169, 70, 29, 12, 5, 2, 1

Offset: 0

Author

Roger L. Bagula, Dec 11 2008

Keywords

• nonn
• tabl

Examples

			Triangle begins as:
  1;
  1, 1;
  1, 2, 1;
  1, 2, 2,  1;
  1, 2, 5,  2,  1;
  1, 2, 5,  5,  2,  1;
  1, 2, 5, 12,  5,  2,  1;
  1, 2, 5, 12, 12,  5,  2,  1;
  1, 2, 5, 12, 29, 12,  5,  2, 1;
  1, 2, 5, 12, 29, 29, 12,  5, 2, 1;
  1, 2, 5, 12, 29, 70, 29, 12, 5, 2, 1;
		

Links

• G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Crossrefs

Cf. A000129, A238375 (row sums).

Programs

Mathematica

(* First program *)
Pell[n_]:= Pell[n]= If[n<2, n, 2*Pell[n-1] + Pell[n-2]];
T[n_, k_]:= Pell[1 + Min[k, n-k]];
Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten (* modified by G. C. Greubel, May 15 2021 *)
(* Second program *)
Table[Fibonacci[1 +Min[k, n-k], 2], {n,0,15}, {k,0,n}]//Flatten (* G. C. Greubel, May 15 2021 *)

Sage

def Pell(n): return n if (n<2) else 2*Pell(n-1) + Pell(n-2)
def T(n,k): return Pell(1+min(k,n-k))
flatten([[T(n,k) for k in (0..n)] for n in (0..15)]) # G. C. Greubel, May 15 2021

Formula

Sum_{k=0..n} T(n,k) = A238375(n). - Philippe Deléham, Feb 27 2014

T(2*n,n) = A000129(n+1). - Philippe Deléham, Feb 27 2014

Extensions

Better name by Philippe Deléham, Feb 27 2014