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

0,1

Comments

Just after A367559 and A368826.

Links

Table of n, a(n) for n=0..65.

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

Example

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).

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 *)

Crossrefs

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

Cf. A023443.

Sequence in context: A307639 A231483 A309656 * A363327 A309657 A296615

Adjacent sequences: A370879 A370880 A370881 * A370883 A370884 A370885

Keyword

sign,tabl

Author

Paul Curtz, Mar 05 2024

Status

approved