A185909 Accumulation array of A185908, by antidiagonals.

1, 2, 3, 3, 7, 6, 4, 11, 14, 10, 5, 15, 23, 23, 15, 6, 19, 32, 38, 34, 21, 7, 23, 41, 54, 56, 47, 28, 8, 27, 50, 70, 80, 77, 62, 36, 9, 31, 59, 86, 105, 110, 101, 79, 45, 10, 35, 68, 102, 130, 145, 144, 128, 98, 55, 11, 39, 77, 118, 155, 181, 190, 182, 158, 119, 66, 12, 43, 86, 134, 180, 217, 238, 240, 224, 191, 142, 78, 13, 47, 95, 150, 205, 253, 287, 301, 295, 270, 227, 167, 91, 14, 51, 104, 166, 230, 289, 336, 364, 370, 355, 320, 266, 194, 105, 15, 55, 113, 182, 255

Offset: 1

Author

Clark Kimberling, Feb 06 2011

Keywords

• nonn
• tabl

Comments

A member of the accumulation chain ... < A185907 < A185908 < A185909 < ...

(See A144112 for definitions of weight array and accumulation array.)

Examples

			Northwest corner:
   1,  2,  3,  4,  5
   3,  7, 11, 15, 19
   6, 14, 23, 32, 41
  10, 23, 38, 54, 70
		

Links

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

Crossrefs

Cf. A144112, A185907, A185908.

diag (1,7,...): A004068.

diag (2,11,...): A033994.

diag (3,14,...): A162147.

Programs

Mathematica

f[n_, 0] := 0; f[0, k_] := 0; (*needed for the weight array*)
f[n_, k_] := Min[n, k] + n - 1;
s[n_, k_] := Sum[f[i, j], {i, 1, n}, {j, 1, k}];
Table[s[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten