A185507 Second accumulation array, T, of the natural number array A000027, by antidiagonals.

1, 4, 5, 11, 19, 15, 25, 49, 55, 35, 50, 105, 136, 125, 70, 91, 200, 280, 300, 245, 126, 154, 350, 515, 600, 575, 434, 210, 246, 574, 875, 1075, 1125, 1001, 714, 330, 375, 894, 1400, 1785, 1975, 1925, 1624, 1110, 495, 550, 1335, 2136, 2800, 3220, 3325, 3080, 2496, 1650, 715, 781, 1925, 3135, 4200, 4970, 5341, 5250, 4680, 3675, 2365, 1001, 1079, 2695, 4455, 6075, 7350, 8134, 8330, 7890, 6825, 5225, 3289, 1365, 1456, 3679, 6160, 8525, 10500, 11886, 12544, 12390, 11400, 9625, 7216, 4459, 1820, 1925, 4914, 8320, 11660

Offset

1,2

Comments

See A144112 (and A185506) for the definition of accumulation array (aa).

Sequence is aa(aa(A000027)).

Links

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

Formula

T(n,k) = k*n*(k+1)*(n+1)*(3*n^2 + (4*k+11)*n + 3*k^2 - k + 16)/144.

Example

Northwest corner:
   1,   4,  11,   25,   50,   91,  154
   5,  19,  49,  105,  200,  350,  574
  15,  55, 136,  280,  515,  875, 1400
  35, 125, 300,  600, 1075, 1785, 2800
  70, 245, 575, 1125, 1975, 3220, 4970

Mathematica

g[n_, k_]:=k*n(k+1)(n+1)(3n^2+(4k+11)n+3k^2-k+16)/144;
TableForm[Table[g[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[g[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

Crossrefs

Cf. A006522 (row 1), A000332 (column 1).

Cf. A000027, A185506, A185508, A185509.

Sequence in context: A118143 A001350 A077238 * A000286 A227620 A036539

Adjacent sequences: A185504 A185505 A185506 * A185508 A185509 A185510

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 29 2011

Status

approved