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

9, 8, 18, 7, 17, 36, 6, 16, 35, 72, 5, 15, 34, 71, 144, 4, 14, 33, 70, 143, 288, 3, 13, 32, 69, 142, 287, 576, 2, 12, 31, 68, 141, 286, 575, 1152, 1, 11, 30, 67, 140, 285, 574, 1151, 2304, 0, 10, 29, 66, 139, 284, 573, 1150, 2303, 4608, -1, 9, 28, 65, 138, 283, 572, 1149, 2302, 4607, 9216

Offset: 0

Author

Paul Curtz, Mar 05 2024

Keywords

• sign
• tabl

Comments

Just after A367559 and A368826.

Examples

			Table begins:
       k=0  1  2  3   4   5
  n=0:   9 18 36 72 144 288 ...
  n=1:   8 17 35 71 143 287 ...
  n=2:   7 16 34 70 142 286 ...
  n=3:   6 15 33 69 141 285 ...
  n=4:   5 14 32 68 140 284 ...
  n=5:   4 13 31 67 139 283 ...
Every line has the signature (3,-2). For n=1: 3*17 - 2*8 = 35.
Main diagonal's difference table:
  9   17   34   69   140   283   570  1145  ...  =  b(n)
  8   17   35   71   143   287   575  1151  ...  =  A052996(n+2)
  9   18   36   72   144   288   576  1152  ...  =  A005010(n)
  ...
b(n+1) - 2*b(n) = A023443(n).
		

Crossrefs

Cf. A000225, A033484, A048491, A005010, A052996, A053209, A083329, A154251, A176449, A304383, A367559, A368826.

Cf. A023443.

Programs

Mathematica

T[n_, k_] := 9*2^k - n; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Amiram Eldar, Mar 06 2024 *)

Formula

T(0,k) = 9*2^k = A005010(k);

T(1,k) = 9*2^k - 1 = A052996(k+2);

T(2,k) = 9*2^k - 2 = A176449(k);

T(3,k) = 9*2^k - 3 = 3*A083329(k);

T(4,k) = 9*2^k - 4 = A053209(k);

T(5,k) = 9*2^k - 5 = A304383(k+3);

T(6,k) = 9*2^k - 6 = 3*A033484(k);

T(7,k) = 9*2^k - 7 = A154251(k+1);

T(8,k) = 9*2^k - 8 = A048491(k);

T(9,k) = 9*2^k - 9 = 3*A000225(k).

G.f.: (9 - 9*y + x*(11*y - 10))/((1 - x)^2*(1 - y)*(1 - 2*y)). - Stefano Spezia, Mar 17 2024