|
| |
|
|
A049777
|
|
Triangular array read by rows: T(m,n) = n + n+1 + ... + m = (m+n)(m-n+1)/2.
|
|
8
|
|
|
|
1, 3, 2, 6, 5, 3, 10, 9, 7, 4, 15, 14, 12, 9, 5, 21, 20, 18, 15, 11, 6, 28, 27, 25, 22, 18, 13, 7, 36, 35, 33, 30, 26, 21, 15, 8, 45, 44, 42, 39, 35, 30, 24, 17, 9, 55, 54, 52, 49, 45, 40, 34, 27, 19, 10, 66, 65, 63, 60, 56, 51, 45, 38, 30, 21, 11, 78, 77, 75, 72, 68, 63, 57, 50
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
COMMENTS
|
Triangle read by rows, T(n,k) = A000217(n) - A000217(k), 0<=k<n. - Philippe Deléham, Mar 07 2013
Subtriangle of triangle in A049780. - Philippe Deléham, Mar 07 2013
|
|
|
LINKS
|
Table of n, a(n) for n=1..74.
|
|
|
FORMULA
|
Partial sums of A002260 row terms, starting from the right; e.g. row 3 of A002260 = (1, 2, 3), giving (6, 5, 3). - Gary W. Adamson, Oct 23 2007
Sum_{k, 0<=k<n}(-1)^k*(2*k+1)*A000203(T(n,k)) = (-1)^(n-1)*A000330(n). - Philippe Deléham, Mar 07 2013
|
|
|
EXAMPLE
|
Rows: {1}; {3,2}; {6,5,3}; ...
|
|
|
MATHEMATICA
|
Flatten[Table[(n+k) (n-k+1)/2, {n, 15}, {k, n}]] (* From Harvey P. Dale, Feb 27 2012 *)
|
|
|
PROG
|
(PARI) {T(n, k) = if( k<1 | n<k, 0, (n + k) * (n - k + 1) / 2 )} /* Michael Somos Oct 06 2007 */
|
|
|
CROSSREFS
|
Row sums = A000330.
Cf. A000217, A002260, A049780, A094728.
Sequence in context: A177828 A090571 A088452 * A193999 A210971 A212000
Adjacent sequences: A049774 A049775 A049776 * A049778 A049779 A049780
|
|
|
KEYWORD
|
nonn,tabl
|
|
|
AUTHOR
|
Clark Kimberling
|
|
|
STATUS
|
approved
|
| |
|
|
