OFFSET
1,2
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened
FORMULA
T(n,k) = (k*n/6)*(2*n^2 + 3*n + 3*k - 2), k >= 1, n >= 1.
EXAMPLE
Northwest corner:
1, 3, 6, 10, 15
5, 12, 21, 32, 45
14, 31, 51, 74, 100
30, 64, 102, 144, 190
MATHEMATICA
f[n_, 0] := 0; f[0, k_] := 0;
f[n_, k_] := n^2 + k - 1;
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 A185812*)
Table[s[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten
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 *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 06 2011
STATUS
approved