A185878 Accumulation array of A185877, by antidiagonals.

1, 4, 2, 11, 10, 3, 24, 28, 18, 4, 45, 60, 51, 28, 5, 76, 110, 108, 80, 40, 6, 119, 182, 195, 168, 115, 54, 7, 176, 280, 318, 300, 240, 156, 70, 8, 249, 408, 483, 484, 425, 324, 203, 88, 9, 340, 570, 696, 728, 680, 570, 420, 256, 108, 10, 451, 770, 963, 1040, 1015, 906, 735, 528, 315, 130, 11, 584, 1012, 1290, 1428, 1440, 1344, 1162, 920, 648, 380, 154, 12

Offset: 1

Author

Clark Kimberling, Feb 05 2011

Keywords

• nonn
• tabl

Comments

A member of the accumulation chain ... < A185879 < A185877 < A185878 < A185880 < ...

See A144112 for the definition of accumulation array.

Examples

			Northwest corner:
  1,  4, 11,  24,  45, ...
  2, 10, 28,  60, 110, ...
  3, 18, 51, 108, 195, ...
  4, 28, 80, 168, 300, ...
  ...
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A144112, A185877, A185879.

Row 1 to 3: A006527, A006331, A064043.

Column 1 to 5: A000027, A028552, A140677, 12*A000096, 5*A130861.

Programs

Mathematica

f[n_, k_] := k*n*(2*k^2 - 3*k + 3*k*n - 3*n + 7)/6; Table[f[n - k + 1, k], {n,10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 21 2017 *)

Formula

T(n,k) = k*n*(2*k^2 -3*k +3*k*n -3*n +7)/6, k>=1, n>=1.