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

Author

Clark Kimberling, Jan 29 2011

Keywords

• nonn
• tabl

Comments

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

Sequence is aa(aa(A000027)).

Examples

			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
		

Links

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

Crossrefs

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

Cf. A000027, A185506, A185508, A185509.

Programs

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

Formula

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