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A185912
Accumulation array of A185910; by antidiagonals.
4
1, 3, 5, 6, 12, 14, 10, 21, 31, 30, 15, 32, 51, 64, 55, 21, 45, 74, 102, 115, 91, 28, 60, 100, 144, 180, 188, 140, 36, 77, 129, 190, 250, 291, 287, 204, 45, 96, 161, 240, 325, 400, 441, 416, 285, 55, 117, 196, 294, 405, 515, 602, 636, 579, 385, 66, 140, 234, 352, 490, 636, 770, 864, 882, 780, 506, 78, 165, 275, 414, 580, 763, 945, 1100, 1194, 1185, 1023, 650, 91, 192, 319, 480, 675, 896, 1127, 1344, 1515, 1600, 1551, 1312, 819, 105
OFFSET
1,2
COMMENTS
A member of the accumulation chain ... < A185910 < A185911 < A185912 < A185913 < ...
(See A144112 for definitions of weight array and accumulation array.)
FORMULA
T(n,k) = (k*n/6)*(2*n^2 + 3*n + 3*k - 2), k >= 1, n >= 1.
EXAMPLE
Northwest corner:
1, 3, 6, 10, 15
5, 12, 21, 32, 45
14, 31, 51, 74, 100
30, 64, 102, 144, 190
MATHEMATICA
f[n_, 0] := 0; f[0, k_] := 0;
f[n_, k_] := n^2 + k - 1;
s[n_, k_] := Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (*accumulation array of {f(n, k)}*)
FullSimplify[s[n, k]] (*formula for A185812*)
Table[s[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten
T[n_, k_] := (k*n/6)*(2*n^2 + 3*n + 3*k - 2) ; Table[T[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 22 2017 *)
CROSSREFS
Row 1 to 2: A000217, A028347.
Column 1 to 3: A000330, A037237, 3*A145066.
Sequence in context: A127577 A280590 A356709 * A100712 A086187 A088082
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 06 2011
STATUS
approved