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A185913
Accumulation array of A185912, by antidiagonals.
4
1, 4, 6, 10, 21, 20, 20, 48, 66, 50, 35, 90, 144, 160, 105, 56, 150, 260, 340, 330, 196, 84, 231, 420, 600, 690, 609, 336, 120, 336, 630, 950, 1200, 1260, 1036, 540, 165, 468, 896, 1400, 1875, 2170, 2128, 1656, 825, 220, 630, 1224, 1960, 2730, 3360, 3640, 3384, 2520, 1210, 286, 825, 1620, 2640, 3780, 4851, 5600, 5760, 5130, 3685, 1716, 364, 1056, 2090, 3450, 5040, 6664, 8036, 8820, 8700, 7480, 5214, 2366, 455
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) = C(k+1,2)*C(n+1,2)*(n^2+3*n+2*k)/6, k>=1, n>=1.
EXAMPLE
Northwest corner:
1.....4.....10.....20.....35
6.....21....48.....90.....150
20....66....144....260....420
50....160...340....600....950
MATHEMATICA
(* The program generates A185912 and its accumulation array A185913 *)
f[n_, k_]:=(k*n/6)(-2+3k+3n+2n^2);
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185912 *)
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}];
FullSimplify[s[n, k]] (* formula for A185913 *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* array A185913 *)
Table[s[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
CROSSREFS
Row 1 to 2: A000292, 3*A005581.
Column 1: A002415.
Sequence in context: A220033 A277455 A320124 * A243119 A277343 A077065
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 06 2011
STATUS
approved