cp's OEIS Frontend

A185912 Accumulation array of A185910; by antidiagonals.

%I A185912 #12 Jul 22 2017 09:15:33
%S A185912 1,3,5,6,12,14,10,21,31,30,15,32,51,64,55,21,45,74,102,115,91,28,60,
%T A185912 100,144,180,188,140,36,77,129,190,250,291,287,204,45,96,161,240,325,
%U A185912 400,441,416,285,55,117,196,294,405,515,602,636,579,385,66,140,234,352,490,636,770,864,882,780,506,78,165,275,414,580,763,945,1100,1194,1185,1023,650,91,192,319,480,675,896,1127,1344,1515,1600,1551,1312,819,105
%N A185912 Accumulation array of A185910; by antidiagonals.
%C A185912 A member of the accumulation chain ... < A185910 < A185911 < A185912 < A185913 < ...
%C A185912 (See A144112 for definitions of weight array and accumulation array.)
%H A185912 G. C. Greubel, <a href="/A185912/b185912.txt">Table of n, a(n) for the first 50 rows, flattened</a>
%F A185912 T(n,k) = (k*n/6)*(2*n^2 + 3*n + 3*k - 2), k >= 1, n >= 1.
%e A185912 Northwest corner:
%e A185912    1,   3,   6,  10,  15
%e A185912    5,  12,  21,  32,  45
%e A185912   14,  31,  51,  74, 100
%e A185912   30,  64, 102, 144, 190
%t A185912 f[n_, 0] := 0; f[0, k_] := 0;
%t A185912 f[n_, k_] := n^2 + k - 1;
%t A185912 s[n_, k_] := Sum[f[i, j], {i, 1, n}, {j, 1, k}];(*accumulation array of {f(n,k)}*)
%t A185912 FullSimplify[s[n, k]]  (*formula for A185812*)
%t A185912 Table[s[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten
%t A185912 T[n_, k_] := (k*n/6)*(2*n^2 + 3*n + 3*k - 2) ; Table[T[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* _G. C. Greubel_, Jul 22 2017 *)
%Y A185912 Cf. A144112, A185910, A185913.
%Y A185912 Row 1 to 2: A000217, A028347.
%Y A185912 Column 1 to 3: A000330, A037237, 3*A145066.
%K A185912 nonn,tabl
%O A185912 1,2
%A A185912 _Clark Kimberling_, Feb 06 2011