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

1,2

Comments

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

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

Links

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

Example

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

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

Crossrefs

Cf. A144112, A185907, A185908.

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

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

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

Sequence in context: A140407 A063670 A253357 * A347533 A193713 A171824

Adjacent sequences: A185906 A185907 A185908 * A185910 A185911 A185912

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 06 2011

Status

approved