%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