A176298 Triangle T(n,k) = 1 + n - floor(n/(k+1)) - floor(n/(n-k+1)) read by rows.

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, 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, 8, 9, 9, 10, 10, 9, 9, 8, 6, 1, 1, 6, 8, 9, 10, 10, 11, 10, 10, 9, 8, 6, 1

Offset

0,8

Comments

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

Links

Indranil Ghosh, Rows 0..125, flattened

Formula

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

Example

Triangle begins as:
  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, 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;

Maple

A176298 := proc(n, m) 1+n-floor(n/(m+1)) - floor(n/(n-m+1)) ; end proc: # R. J. Mathar, Jan 29 2011

Mathematica

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

Prog

(Python)
#Program to generate the b-file
i=0
for n in range(126):
    for m in range(n+1):
        print(str(i)+" "+str(1+n-(n/(m+1))-(n/(n-m+1))))
        i+=1 # Indranil Ghosh, Feb 20 2017
(PARI) T(n, k) = 1+n -floor(n/(k+1)) -floor(n/(n-k+1)); \\ G. C. Greubel, Nov 26 2019
(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
(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
(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

Crossrefs

Cf. A006218.

Sequence in context: A115092 A172281 A304945 * A259575 A370062 A169623

Adjacent sequences: A176295 A176296 A176297 * A176299 A176300 A176301

Keyword

nonn,tabl,easy

Author

Roger L. Bagula, Apr 14 2010

Status

approved