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A185880 Second accumulation array of A185877, by antidiagonals. 4
1, 5, 3, 16, 17, 6, 40, 56, 38, 10, 85, 140, 128, 70, 15, 161, 295, 320, 240, 115, 21, 280, 553, 670, 600, 400, 175, 28, 456, 952, 1246, 1250, 1000, 616, 252, 36, 705, 1536, 2128, 2310, 2075, 1540, 896, 348, 45, 1045, 2355, 3408, 3920, 3815, 3185, 2240, 1248, 465, 55, 1496, 3465, 5190, 6240, 6440, 5831, 4620, 3120, 1680, 605, 66, 2080, 4928, 7590, 9450, 10200, 9800, 8428, 6420, 4200, 2200 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
A member of the accumulation chain ... < A185879 < A185877 < A185878 < A185880 < ... See A144112 for the definition of accumulation array.
LINKS
FORMULA
T(n,k) = C(k,2)*C(n,2)*(3*k^2+4*k*n-k-4*n+16)/18, k>=1, n>=1.
EXAMPLE
Northwest corner:
1, 5, 16, 40, 85
3, 17, 56, 140, 295
6, 38, 128, 320, 670
10, 70, 240, 600, 1250
MATHEMATICA
(* This program generates A185878 first and then generates A185880 as the accumulation array of A185878. *)
f[n_, k_]:=(k*n/6)(7-3k+2k^2-3n+3kn);
TableForm[Table[f[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185878 *)
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}];
FullSimplify[s[n, k]]
TableForm[Table[s[n, k], {n, 1, 10}, {k, 1, 15}]] (* A185880 *)
f[n_, k_] := (1/72)*k*(1 + k)*n*(1 + n)*(16 - k + 3 *k^2 + 4 *(-1 + k) *n); Table[f[n - k + 1, k], {n, 10}, {k, n, 1, -1}] // Flatten (* G. C. Greubel, Jul 21 2017 *)
CROSSREFS
Antidiagonal sums: A037235.
diag (1,5,...): A056108 (4th spoke on hexagonal wheel);
diag (3,11,...): A056106 (2nd spoke on hexagonal wheel);
diag (7,19,...): A003215 (hex numbers);
diag (13,29,...): A144391.
Sequence in context: A199005 A217415 A213571 * A292243 A105201 A184537
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Feb 05 2011
STATUS
approved

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Last modified May 24 01:38 EDT 2024. Contains 372768 sequences. (Running on oeis4.)