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%I #12 Jul 17 2017 02:31:54
%S 1,5,7,16,24,22,38,59,65,50,75,120,141,136,95,131,215,262,274,245,161,
%T 210,352,440,480,470,400,252,316,539,687,770,790,741,609,372,453,784,
%U 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
%N Accumulation array of the (odd,odd)-polka dot array A185868, by antidiagonals.
%C See A144112 for the definition of accumulation array.
%H G. C. Greubel, <a href="/A185872/b185872.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F T(n,k) = (k*n/6)*(4*n^2 + 6*n*k + 4*k^2 - 3*n - 9*k + 4), k>=1, n>=1.
%e Northwest corner:
%e 1, 5, 16, 38, 75
%e 7, 24, 59, 120, 215
%e 22, 54, 141, 262, 440
%e 50, 136, 174, 480, 770
%t f[n_,k_]:=2n-1+(2n+2k-4)(2n+2k-3)/2;
%t TableForm[Table[f[n,k],{n,1,10},{k,1,15}]] (* A185868 *)
%t Table[f[n-k+1,k],{n,14},{k,n,1,-1}]//Flatten
%t s[n_,k_]:=Sum[f[i,j],{i,1,n},{j,1,k}]; (* accumulation array of {f(n,k)} *)
%t FullSimplify[s[n,k]] (*formula for A185872 *)
%t g[n_]:=Sum[f[n+1-k,k],{k,1,n}];
%t Table[g[n],{n,50}] (* A185872 *)
%t TableForm[Table[s[n,k],{n,1,10},{k,1,15}]]
%Y Cf. A185868.
%Y Row 1: A174723; column 1: A002412.
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Feb 05 2011
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