A185509 Fourth accumulation array, T, of the natural number array A000027, by antidiagonals.

1, 6, 7, 22, 41, 28, 63, 146, 161, 84, 154, 406, 561, 476, 210, 336, 966, 1526, 1631, 1176, 462, 672, 2058, 3556, 4361, 3976, 2562, 924, 1254, 4032, 7434, 9996, 10486, 8568, 5082, 1716, 2211, 7392, 14322, 20580, 23716, 22344, 16842, 9372, 3003, 3718, 12837, 25872, 39102, 48216, 49980, 43512, 30822, 16302, 5005, 6006, 21307, 44352, 69762, 90552, 100548, 96432, 79002, 53262, 27027, 8008, 9373, 34034, 72787, 118272, 159852

Offset

1,2

Comments

See A144112 (and A185506) for the definition of rectangular sum array (aa).

Sequence is aa(aa(aa(aa(A000027)))).

Links

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

Formula

T(n,k) = F*(5*n^2 + (6*k + 39)*n + 5*k^2 + 9*k + 86), where

F = k*(k+1)*(k+2)*(k+3)*n*(n+1)*(n+2)*(n+3)/86400.

Example

Northwest corner:
1.....6....22....63...154
7....41...146...406...966
28..161...561..1526..3556
84..476..1631..4361..9996

Mathematica

u[n_, k_]:=k(k+1)(k+2)(k+3)n(n+1)(n+2)(n+3)(5n^2+(6k+39)n+5k^2+9k+86)/86400
TableForm[Table[u[n, k], {n, 1, 10}, {k, 1, 15}]]
Table[u[n-k+1, k], {n, 14}, {k, n, 1, -1}]//Flatten

Crossrefs

Cf. A000027, A185506, A185507, A185508.

Cf. A000579 (column 1), A257200 (row 1).

Sequence in context: A048062 A295729 A081284 * A099572 A288705 A287097

Adjacent sequences: A185506 A185507 A185508 * A185510 A185511 A185512

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 29 2011

Status

approved