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
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
Programs
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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