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

0,2

Comments

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

Links

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

Example

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; ...

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 *)

Prog

(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
(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
(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
(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

Crossrefs

Cf. A046854, A065941, A001595.

Sequence in context: A029315 A070080 A230196 * A132749 A271106 A273673

Adjacent sequences: A131397 A131398 A131399 * A131401 A131402 A131403

Keyword

nonn,tabl

Author

Gary W. Adamson, Jul 06 2007

Extensions

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

Status

approved