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

Author

Clark Kimberling, Feb 05 2011

Keywords

• nonn
• tabl

Comments

See A144112 for the definition of accumulation array.

Examples

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

Links

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

Crossrefs

Cf. A185868.

Row 1: A174723; column 1: A002412.

Programs

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}]]

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.