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

1,2

Comments

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

See A144112 for the definition of accumulation array.

Links

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A144112, A185877, A185879.

Row 1 to 3: A006527, A006331, A064043.

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

Sequence in context: A318784 A154699 A213568 * A182870 A094406 A142706

Adjacent sequences: A185875 A185876 A185877 * A185879 A185880 A185881

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 05 2011

Status

approved