A185508 Third accumulation array, T, of the natural number array A000027, by antidiagonals.

1, 5, 6, 16, 29, 21, 41, 89, 99, 56, 91, 219, 295, 259, 126, 182, 469, 705, 755, 574, 252, 336, 910, 1470, 1765, 1645, 1134, 462, 582, 1638, 2786, 3605, 3780, 3206, 2058, 792, 957, 2778, 4914, 6706, 7595, 7266, 5754, 3498, 1287, 1507, 4488, 8190, 11634, 13916, 14406, 12894, 9690, 5643, 2002, 2288, 6963, 13035, 19110, 23814, 26068, 25284, 21510, 15510, 8723, 3003, 3367, 10439, 19965, 30030, 38640, 44100

Offset

1,2

Comments

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

Sequence is aa(aa(aa(A000027))).

Links

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

Formula

T(n,k) = F*(4n^2 + (5k+23)n + 4k^2 + 3k+41), where F = k(k+1)(k+2)n(n+1)(n+2)/2880.

Example

Northwest corner:
   1    5   16   41   91  182
   6   29   89  219  469  910
  21   99  295  705 1470 2786
  56  259  755 1765 3605 6706

Mathematica

h[n_, k_]:=k(k+1)(k+2)n(n+1)(n+2)*(4n^2+(5k+23)n+4k^2+3k+41)/2880;
TableForm[Table[h[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[h[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

Prog

(PARI) {h(n, k) = k*(k+1)*(k+2)*n*(n+1)*(n+2)*(4*n^2+(5*k+23)*n +4*k^2 +3*k + 41)/2880}; for(n=1, 10, for(k=1, n, print1(h(k, n-k+1), ", "))) \\ G. C. Greubel, Nov 23 2017

Crossrefs

Cf. A000027, A185506, A185507, A185509.

Cf. A000389 (column 1), A257199 (row 1).

Sequence in context: A186696 A034454 A246715 * A358091 A257338 A059013

Adjacent sequences: A185505 A185506 A185507 * A185509 A185510 A185511

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 29 2011

Status

approved