A131400 A046854 + A065941 - I (Identity matrix).

1, 2, 1, 2, 2, 1, 2, 3, 3, 1, 2, 3, 6, 3, 1, 2, 4, 7, 7, 4, 1, 2, 4, 11, 8, 11, 4, 1, 2, 5, 12, 15, 15, 12, 5, 1, 2, 5, 17, 16, 30, 16, 17, 5, 1, 2, 6, 18, 27, 36, 36, 27, 18, 6, 1, 2, 6, 24, 28, 63, 42, 63, 28, 24, 6, 1, 2, 7, 25, 44, 71, 84, 84, 71, 44, 25, 7, 1

Offset: 0

Author

Gary W. Adamson, Jul 06 2007

Keywords

• nonn
• tabl

Comments

Row sums = A001595: (1, 3, 5, 9, 15, 25, 41, 67,...).

Examples

			First few rows of the triangle are:
  1;
  2, 1;
  2, 2,  1;
  2, 3,  3, 1;
  2, 3,  6, 3,  1;
  2, 4,  7, 7,  4, 1;
  2, 4, 11, 8, 11, 4, 1; ...
		

Links

• G. C. Greubel, Rows n = 0..100 of triangle, flattened

Crossrefs

Cf. A046854, A065941, A001595.

Programs

GAP

B:=Binomial;;
T:= function(n,k)
    if k=n then return 1;
    else return B(Int((n+k)/2), k) + B(n - Int((k+1)/2), Int(k/2));
    fi;
  end;
Flat(List([0..12], n-> List([0..n], k-> T(n,k) ))); # G. C. Greubel, Jul 13 2019

Magma

B:=Binomial; [k eq n select 1 else B(Floor((n+k)/2), k) + B(n - Floor((k+1)/2), Floor(k/2)): k in [0..n], n in [0..12]]; // G. C. Greubel, Jul 13 2019

Mathematica

With[{B = Binomial}, Table[If[k==n, 1, B[Floor[(n+k)/2], k] + B[n - Floor[(k+1)/2], Floor[k/2]]], {n,0,12}, {k,0,n}]]//Flatten (* G. C. Greubel, Jul 13 2019 *)

PARI

b=binomial; T(n,k) = if(k==n, 1, b((n+k)\2, k) + b(n - (k+1)\2, k\2));
for(n=0,12, for(k=0,n, print1(T(n,k), ", ", ))) \\ G. C. Greubel, Jul 13 2019

Sage

def T(n, k):
    b=binomial;
    if (k==n): return 1
    else: return b(floor((n+k)/2), k) + b(n - floor((k+1)/2), floor(k/2))
[[T(n, k) for k in (0..n)] for n in (0..12)] # G. C. Greubel, Jul 13 2019

Extensions

More terms added by G. C. Greubel, Jul 13 2019