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A370882 Square array T(n,k) = 9*2^k - n read by ascending antidiagonals.

%I A370882 #37 Mar 18 2024 11:46:20
%S A370882 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 A370882 69,142,287,576,2,12,31,68,141,286,575,1152,1,11,30,67,140,285,574,
%U A370882 1151,2304,0,10,29,66,139,284,573,1150,2303,4608,-1,9,28,65,138,283,572,1149,2302,4607,9216
%N A370882 Square array T(n,k) = 9*2^k - n read by ascending antidiagonals.
%C A370882 Just after A367559 and A368826.
%F A370882 T(0,k) = 9*2^k     =   A005010(k);
%F A370882 T(1,k) = 9*2^k - 1 =   A052996(k+2);
%F A370882 T(2,k) = 9*2^k - 2 =   A176449(k);
%F A370882 T(3,k) = 9*2^k - 3 = 3*A083329(k);
%F A370882 T(4,k) = 9*2^k - 4 =   A053209(k);
%F A370882 T(5,k) = 9*2^k - 5 =   A304383(k+3);
%F A370882 T(6,k) = 9*2^k - 6 = 3*A033484(k);
%F A370882 T(7,k) = 9*2^k - 7 =   A154251(k+1);
%F A370882 T(8,k) = 9*2^k - 8 =   A048491(k);
%F A370882 T(9,k) = 9*2^k - 9 = 3*A000225(k).
%F A370882 G.f.: (9 - 9*y + x*(11*y - 10))/((1 - x)^2*(1 - y)*(1 - 2*y)). - _Stefano Spezia_, Mar 17 2024
%e A370882 Table begins:
%e A370882        k=0  1  2  3   4   5
%e A370882   n=0:   9 18 36 72 144 288 ...
%e A370882   n=1:   8 17 35 71 143 287 ...
%e A370882   n=2:   7 16 34 70 142 286 ...
%e A370882   n=3:   6 15 33 69 141 285 ...
%e A370882   n=4:   5 14 32 68 140 284 ...
%e A370882   n=5:   4 13 31 67 139 283 ...
%e A370882 Every line has the signature (3,-2). For n=1: 3*17 - 2*8 = 35.
%e A370882 Main diagonal's difference table:
%e A370882   9   17   34   69   140   283   570  1145  ...  =  b(n)
%e A370882   8   17   35   71   143   287   575  1151  ...  =  A052996(n+2)
%e A370882   9   18   36   72   144   288   576  1152  ...  =  A005010(n)
%e A370882   ...
%e A370882 b(n+1) - 2*b(n) = A023443(n).
%t A370882 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 A370882 Cf. A000225, A033484, A048491, A005010, A052996, A053209, A083329, A154251, A176449, A304383, A367559, A368826.
%Y A370882 Cf. A023443.
%K A370882 sign,tabl
%O A370882 0,1
%A A370882 _Paul Curtz_, Mar 05 2024