A185872 Accumulation array of the (odd,odd)-polka dot array A185868, by antidiagonals.

1, 5, 7, 16, 24, 22, 38, 59, 65, 50, 75, 120, 141, 136, 95, 131, 215, 262, 274, 245, 161, 210, 352, 440, 480, 470, 400, 252, 316, 539, 687, 770, 790, 741, 609, 372, 453, 784, 1015, 1160, 1225, 1208, 1099, 880, 525, 625, 1095, 1436, 1666, 1795, 1825, 1750, 1556, 1221, 715, 836, 1480, 1962, 2304, 2520, 2616, 2590, 2432, 2124, 1640, 946, 1090, 1947, 2605, 3090, 3420, 3605, 3647, 3540

Offset

1,2

Comments

See A144112 for the definition of accumulation array.

Links

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

Formula

T(n,k) = (k*n/6)*(4*n^2 + 6*n*k + 4*k^2 - 3*n - 9*k + 4), k>=1, n>=1.

Example

Northwest corner:
   1,   5,  16,  38,  75
   7,  24,  59, 120, 215
  22,  54, 141, 262, 440
  50, 136, 174, 480, 770

Mathematica

f[n_, k_]:=2n-1+(2n+2k-4)(2n+2k-3)/2;
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185868 *)
Table[f[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten
s[n_, k_]:=Sum[f[i, j], {i, 1, n}, {j, 1, k}]; (* accumulation array of {f(n, k)} *)
FullSimplify[s[n, k]] (*formula for A185872 *)
g[n_]:=Sum[f[n+1-k, k], {k, 1, n}];
Table[g[n], {n, 50}] (* A185872 *)
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]]

Crossrefs

Cf. A185868.

Row 1: A174723; column 1: A002412.

Sequence in context: A218623 A279175 A279875 * A186710 A276717 A374777

Adjacent sequences: A185869 A185870 A185871 * A185873 A185874 A185875

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 05 2011

Status

approved