A185880 Second accumulation array of A185877, by antidiagonals.

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

Offset

1,2

Comments

A member of the accumulation chain ... < A185879 < A185877 < A185878 < A185880 < ... See A144112 for the definition of accumulation array.

Links

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

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

Cf. A144112, A185877, A185878.

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

Adjacent sequences: A185877 A185878 A185879 * A185881 A185882 A185883

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 05 2011

Status

approved