A238392 Triangle read by rows: each row is an initial segment of the terms of A000123 followed by its reflection.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 2, 4, 4, 2, 1, 1, 2, 4, 6, 4, 2, 1, 1, 2, 4, 6, 6, 4, 2, 1, 1, 2, 4, 6, 10, 6, 4, 2, 1, 1, 2, 4, 6, 10, 10, 6, 4, 2, 1, 1, 2, 4, 6, 10, 14, 10, 6, 4, 2, 1, 1, 2, 4, 6, 10, 14, 14, 10, 6, 4, 2, 1, 1, 2, 4, 6, 10, 14, 20, 14, 10, 6, 4, 2, 1

Offset: 0

Author

Philippe Deléham, Feb 26 2014

Keywords

• easy
• nonn
• tabl

Comments

Triangle read by rows: each row is an initial segment of the terms of A000123 followed by its reflection.

Examples

			Triangle begins:
  1;
  1, 1;
  1, 2, 1;
  1, 2, 2, 1;
  1, 2, 4, 2,  1;
  1, 2, 4, 4,  2,  1;
  1, 2, 4, 6,  4,  2,  1;
  1, 2, 4, 6,  6,  4,  2,  1;
  1, 2, 4, 6, 10,  6,  4,  2,  1;
  1, 2, 4, 6, 10, 10,  6,  4,  2,  1;
  1, 2, 4, 6, 10, 14, 10,  6,  4,  2, 1;
  1, 2, 4, 6, 10, 14, 14, 10,  6,  4, 2, 1;
  1, 2, 4, 6, 10, 14, 20, 14, 10,  6, 4, 2, 1;
  1, 2, 4, 6, 10, 14, 20, 20, 14, 10, 6, 4, 2, 1;
		

Links

• Indranil Ghosh, Rows 0..125, flattened

Crossrefs

Cf. A000123, A004197.

Programs

Mathematica

a[n_] := If[n==0,  1, a[n - 1] + a[Floor[n/2]]]; Flatten[Table[a[Min[k, n - k]], {n, 0, 13}, {k, 0, n}]] (* Indranil Ghosh, Mar 14 2017 *)

PARI

a(n) = if(n==0, 1, a(n-1) + a(floor(n/2)));
tabl(nn) = {for(n=0, nn, for(k=0, n, print1(a(min(k, n - k)),", ");); print(););};
tabl(13); \\ Indranil Ghosh, Mar 14 2017

Python

def a(n): return 1 if n==0 else a(n - 1) + a(n//2)
i=0
for n in range(0, 126):
    for k in range(0, n+1):
        print(str(i)+" "+str(a(min(k, n - k))))
        i+=1 # Indranil Ghosh, Mar 14 2017

Formula

T(n,k) = A000123(min(k,n-k)).

Sum_{k=0..n} T(n,k) = A000123(n).

T(2*n,n) = A000123(n).