A176298 - OEIS

%I #21 Sep 08 2022 08:45:52

%S 1,1,1,1,1,1,1,2,2,1,1,2,3,2,1,1,3,4,4,3,1,1,3,4,5,4,3,1,1,4,5,6,6,5,

%T 4,1,1,4,6,6,7,6,6,4,1,1,5,6,7,8,8,7,6,5,1,1,5,7,8,8,9,8,8,7,5,1,1,6,

%U 8,9,9,10,10,9,9,8,6,1,1,6,8,9,10,10,11,10,10,9,8,6,1

%N Triangle T(n,k) = 1 + n - floor(n/(k+1)) - floor(n/(n-k+1)) read by rows.

%C Row sums are (n+1)^2 - 2*A006218(n) = {1, 2, 3, 6, 9, 16, 21, 32, 41, 54, 67, ...}.

%H Indranil Ghosh, <a href="/A176298/b176298.txt">Rows 0..125, flattened</a>

%F T(n,k) = T(n,n-k).

%e Triangle begins as:

%e   1;

%e   1, 1;

%e   1, 1, 1;

%e   1, 2, 2, 1;

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

%e   1, 3, 4, 4, 3, 1;

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

%e   1, 4, 5, 6, 6, 5, 4, 1;

%e   1, 4, 6, 6, 7, 6, 6, 4, 1;

%e   1, 5, 6, 7, 8, 8, 7, 6, 5, 1;

%e   1, 5, 7, 8, 8, 9, 8, 8, 7, 5, 1;

%p A176298 := proc(n,m) 1+n-floor(n/(m+1)) - floor(n/(n-m+1)) ; end proc: # _R. J. Mathar_, Jan 29 2011

%t T[n_, k_]:= 1+n -Floor[n/(k+1)] -Floor[n/(n-k+1)]; Table[T[n, k], {n,0,15}, {k,0,n}]//Flatten

%o (Python)

%o #Program to generate the b-file

%o i=0

%o for n in range(126):

%o     for m in range(n+1):

%o         print(str(i)+" "+str(1+n-(n/(m+1))-(n/(n-m+1))))

%o         i+=1 # _Indranil Ghosh_, Feb 20 2017

%o (PARI) T(n,k) = 1+n -floor(n/(k+1)) -floor(n/(n-k+1)); \\ _G. C. Greubel_, Nov 26 2019

%o (Magma) [1+n -Floor(n/(k+1)) -Floor(n/(n-k+1)): k in [0..n], n in [0..15]]; // _G. C. Greubel_, Nov 26 2019

%o (Sage) [[1+n -(n//(k+1)) -(n//(n-k+1)) for k in (0..n)] for n in (0..15)] # _G. C. Greubel_, Nov 26 2019

%o (GAP) Flat(List([0..15], n-> List([0..n], k-> 1+n -Int(n/(k+1)) -Int(n/(n-k+1)) ))); # _G. C. Greubel_, Nov 26 2019

%Y Cf. A006218.

%K nonn,tabl,easy

%O 0,8

%A _Roger L. Bagula_, Apr 14 2010