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A176298
Triangle T(n,k) = 1 + n - floor(n/(k+1)) - floor(n/(n-k+1)) read by rows.
4
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
KEYWORD
nonn,tabl,easy
AUTHOR
Roger L. Bagula, Apr 14 2010
STATUS
approved