A255044 - OEIS

%I #7 Feb 14 2015 23:59:07

%S 0,1,4,2,13,40,3,22,121,364,4,31,202,1093,3280,5,40,283,1822,9841,

%T 29524,6,49,364,2551,16402,88573,265720,7,58,445,3280,22963,147622,

%U 797161,2391484,8,67,526,4009,29524,206671,1328602,7174453,21523360

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

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

%F 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.

%e Array begins:

%e .   0   4   40   364   3280   29524   265720   2391484   21523360

%e .   1  13  121  1093   9841   88573   797161   7174453   64570081

%e .   2  22  202  1822  16402  147622  1328602  11957422  107616802

%e .   3  31  283  2551  22963  206671  1860043  16740391  150663523

%e .   4  40  364  3280  29524  265720  2391484  21523360  193710244

%e .   5  49  445  4009  36085  324769  2922925  26306329  236756965

%e .   6  58  526  4738  42646  383818  3454366  31089298  279803686

%e .   7  67  607  5467  49207  442867  3985807  35872267  322850407

%e .   8  76  688  6196  55768  501916  4517248  40655236  365897128

%t (* Array: *)

%t Grid[Table[((2*n + 1)*9^k - 1)/2, {n, 0, 8}, {k, 0, 8}]]

%t (* Array antidiagonals flattened: *)

%t Flatten[Table[((2*(n - k) + 1)*9^k - 1)/2, {n, 0, 8}, {k, 0, n}]]

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

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

%K nonn,tabl

%O 0,3

%A _L. Edson Jeffery_, Feb 13 2015