A141675 - OEIS

%I #16 Apr 08 2024 09:14:30

%S 1,2,1,3,2,1,8,3,2,1,5,4,3,2,1,18,10,4,3,2,1,7,6,5,4,3,2,1,32,7,12,5,

%T 4,3,2,1,9,24,7,6,5,4,3,2,1,50,9,8,14,6,5,4,3,2,1

%N Triangle, T(n, k) = n*(n-k+1)/(k+1) if n mod k+1 = 0, otherwise T(n, k) = n-k+1, read by rows.

%H G. C. Greubel, <a href="/A141675/b141675.txt">Rows n=1..100 of triangle, flattened</a>

%F T(n, k) = n*(n-k+1)/(k+1) if n mod k+1 = 0, otherwise T(n, k) = n-k+1.

%e Triangle begins as:

%e    1;

%e    2,  1;

%e    3,  2,  1;

%e    8,  3,  2,  1;

%e    5,  4,  3,  2,  1;

%e   18, 10,  4,  3,  2,  1;

%e    7,  6,  5,  4,  3,  2,  1;

%e   32,  7, 12,  5,  4,  3,  2,  1;

%e    9, 24,  7,  6,  5,  4,  3,  2,  1;

%e   50,  9,  8, 14,  6,  5,  4,  3,  2,  1;

%t T[n_,k_]:= (n-k+1)*If[Mod[n,k+1]==0,n/(k+1),1];

%t Table[T[n,k], {n,12}, {k,n}]//Flatten

%o (Magma)

%o A141675:= func< n,k | (n mod (k+1)) eq 0 select n*(n-k+1)/(k+1) else n-k+1 >;

%o [A141675(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Apr 06 2024

%o (SageMath)

%o def A141675(n,k): return n*(n-k+1)/(k+1) if n%(k+1)==0 else n-k+1

%o flatten([[A141675(n,k) for k in range(1,n+1)] for n in range(1,13)]) # _G. C. Greubel_, Apr 06 2024

%Y Cf. A126988.

%K nonn

%O 1,2

%A _Roger L. Bagula_ and _Gary W. Adamson_, Sep 06 2008

%E Edited by _G. C. Greubel_, Apr 06 2024