A131400 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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:

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;