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A129234
Triangle read by rows: T(n,k) = n/k + k - 1 if n mod k = 0; otherwise T(n,k)=0 (1 <= k <= n).
6
1, 2, 2, 3, 0, 3, 4, 3, 0, 4, 5, 0, 0, 0, 5, 6, 4, 4, 0, 0, 6, 7, 0, 0, 0, 0, 0, 7, 8, 5, 0, 5, 0, 0, 0, 8, 9, 0, 5, 0, 0, 0, 0, 0, 9, 10, 6, 0, 0, 6, 0, 0, 0, 0, 10, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 12, 7, 6, 6, 0, 7, 0, 0, 0, 0, 0, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 14, 8, 0, 0, 0, 0, 8, 0, 0, 0
OFFSET
1,2
COMMENTS
Row sums = A129235: (1, 4, 6, 11, 10, 20, 14, ...). Moebius transform of A129234 = A129236. Inverse Moebius transform of A129234 = A129237.
FORMULA
G.f. = G(t,z) = Sum_{k>=1} t^k*z^k*(k-(k-1)*z^k)/(1-z^k)^2. - Emeric Deutsch, Apr 17 2007
EXAMPLE
First few rows of the triangle:
1;
2, 2;
3, 0, 3;
4, 3, 0, 4;
5, 0, 0, 0, 5;
6, 4, 4, 0, 0, 6;
7, 0, 0, 0, 0, 0, 7;
...
MAPLE
T:=proc(n, k) if n mod k = 0 then n/k+k-1 else 0 fi end: for n from 1 to 16 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form - Emeric Deutsch, Apr 17 2007
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Apr 05 2007
EXTENSIONS
Edited by Emeric Deutsch, Apr 17 2007
STATUS
approved