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%I #37 Mar 18 2024 11:46:20
%S 9,8,18,7,17,36,6,16,35,72,5,15,34,71,144,4,14,33,70,143,288,3,13,32,
%T 69,142,287,576,2,12,31,68,141,286,575,1152,1,11,30,67,140,285,574,
%U 1151,2304,0,10,29,66,139,284,573,1150,2303,4608,-1,9,28,65,138,283,572,1149,2302,4607,9216
%N Square array T(n,k) = 9*2^k - n read by ascending antidiagonals.
%C Just after A367559 and A368826.
%F T(0,k) = 9*2^k = A005010(k);
%F T(1,k) = 9*2^k - 1 = A052996(k+2);
%F T(2,k) = 9*2^k - 2 = A176449(k);
%F T(3,k) = 9*2^k - 3 = 3*A083329(k);
%F T(4,k) = 9*2^k - 4 = A053209(k);
%F T(5,k) = 9*2^k - 5 = A304383(k+3);
%F T(6,k) = 9*2^k - 6 = 3*A033484(k);
%F T(7,k) = 9*2^k - 7 = A154251(k+1);
%F T(8,k) = 9*2^k - 8 = A048491(k);
%F T(9,k) = 9*2^k - 9 = 3*A000225(k).
%F G.f.: (9 - 9*y + x*(11*y - 10))/((1 - x)^2*(1 - y)*(1 - 2*y)). - _Stefano Spezia_, Mar 17 2024
%e Table begins:
%e k=0 1 2 3 4 5
%e n=0: 9 18 36 72 144 288 ...
%e n=1: 8 17 35 71 143 287 ...
%e n=2: 7 16 34 70 142 286 ...
%e n=3: 6 15 33 69 141 285 ...
%e n=4: 5 14 32 68 140 284 ...
%e n=5: 4 13 31 67 139 283 ...
%e Every line has the signature (3,-2). For n=1: 3*17 - 2*8 = 35.
%e Main diagonal's difference table:
%e 9 17 34 69 140 283 570 1145 ... = b(n)
%e 8 17 35 71 143 287 575 1151 ... = A052996(n+2)
%e 9 18 36 72 144 288 576 1152 ... = A005010(n)
%e ...
%e b(n+1) - 2*b(n) = A023443(n).
%t T[n_, k_] := 9*2^k - n; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Mar 06 2024 *)
%Y Cf. A000225, A033484, A048491, A005010, A052996, A053209, A083329, A154251, A176449, A304383, A367559, A368826.
%Y Cf. A023443.
%K sign,tabl
%O 0,1
%A _Paul Curtz_, Mar 05 2024
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