A255044 Array A read by upward antidiagonals: A(n,k) = ((2*n+1)*9^k-1)/2, n,k >= 0.

0, 1, 4, 2, 13, 40, 3, 22, 121, 364, 4, 31, 202, 1093, 3280, 5, 40, 283, 1822, 9841, 29524, 6, 49, 364, 2551, 16402, 88573, 265720, 7, 58, 445, 3280, 22963, 147622, 797161, 2391484, 8, 67, 526, 4009, 29524, 206671, 1328602, 7174453, 21523360

Offset

0,3

Links

Table of n, a(n) for n=0..44.

Formula

G.f. for row n: (n+(4-n)*x)/((1-x)(1-9*x)).

Recurrence for row n: A(n,k) = 10*A(n,k-1)-9*A(n,k-2), k >= 2, A(n,0) = n, A(n,1) = 9*n+4.

Example

Array begins:
.   0   4   40   364   3280   29524   265720   2391484   21523360
.   1  13  121  1093   9841   88573   797161   7174453   64570081
.   2  22  202  1822  16402  147622  1328602  11957422  107616802
.   3  31  283  2551  22963  206671  1860043  16740391  150663523
.   4  40  364  3280  29524  265720  2391484  21523360  193710244
.   5  49  445  4009  36085  324769  2922925  26306329  236756965
.   6  58  526  4738  42646  383818  3454366  31089298  279803686
.   7  67  607  5467  49207  442867  3985807  35872267  322850407
.   8  76  688  6196  55768  501916  4517248  40655236  365897128

Mathematica

(* Array: *)
Grid[Table[((2*n + 1)*9^k - 1)/2, {n, 0, 8}, {k, 0, 8}]]
(* Array antidiagonals flattened: *)
Flatten[Table[((2*(n - k) + 1)*9^k - 1)/2, {n, 0, 8}, {k, 0, n}]]

Crossrefs

Cf. A191681, A096053, A255043, A198964, A198969 (rows 0-3 and 5).

Cf. A138894 (1/2 of row 2).

Sequence in context: A193849 A064308 A330314 * A248249 A161134 A184183

Adjacent sequences: A255041 A255042 A255043 * A255045 A255046 A255047

Keyword

nonn,tabl

Author

L. Edson Jeffery, Feb 13 2015

Status

approved