OFFSET
0,1
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
KEYWORD
sign,tabl
AUTHOR
Paul Curtz, Mar 05 2024
STATUS
approved