A131400 - OEIS

%I #8 Sep 08 2022 08:45:31

%S 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,

%T 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,

%U 63,42,63,28,24,6,1,2,7,25,44,71,84,84,71,44,25,7,1

%N A046854 + A065941 - I (Identity matrix).

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

%H G. C. Greubel, <a href="/A131400/b131400.txt">Rows n = 0..100 of triangle, flattened</a>

%e First few rows of the triangle are:

%e   1;

%e   2, 1;

%e   2, 2,  1;

%e   2, 3,  3, 1;

%e   2, 3,  6, 3,  1;

%e   2, 4,  7, 7,  4, 1;

%e   2, 4, 11, 8, 11, 4, 1; ...

%t 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 *)

%o (PARI) b=binomial; T(n,k) = if(k==n, 1, b((n+k)\2, k) + b(n - (k+1)\2, k\2));

%o for(n=0,12, for(k=0,n, print1(T(n,k), ", ", ))) \\ _G. C. Greubel_, Jul 13 2019

%o (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

%o (Sage)

%o def T(n, k):

%o     b=binomial;

%o     if (k==n): return 1

%o     else: return b(floor((n+k)/2), k) + b(n - floor((k+1)/2), floor(k/2))

%o [[T(n, k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, Jul 13 2019

%o (GAP)

%o B:=Binomial;;

%o T:= function(n,k)

%o     if k=n then return 1;

%o     else return B(Int((n+k)/2), k) + B(n - Int((k+1)/2), Int(k/2));

%o     fi;

%o   end;

%o Flat(List([0..12], n-> List([0..n], k-> T(n,k) ))); # _G. C. Greubel_, Jul 13 2019

%Y Cf. A046854, A065941, A001595.

%K nonn,tabl

%O 0,2

%A _Gary W. Adamson_, Jul 06 2007

%E More terms added by _G. C. Greubel_, Jul 13 2019