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A355668 Array read by upwards antidiagonals T(n,k) = J(k) + n*J(k+1) where J(n) = A001045(n) is the Jacobsthal numbers.

%I A355668 #28 Jul 14 2022 22:55:20
%S A355668 0,1,1,2,2,1,3,3,4,3,4,4,7,8,5,5,5,10,13,16,11,6,6,13,18,27,32,21,7,7,
%T A355668 16,23,38,53,64,43,8,8,19,28,49,74,107,128,85,9,9,22,33,60,95,150,213,
%U A355668 256,171,10,10,25,38,71,116,193,298,427,512,341
%N A355668 Array read by upwards antidiagonals T(n,k) = J(k) + n*J(k+1) where J(n) = A001045(n) is the Jacobsthal numbers.
%F A355668 T(n, k) = (2^k - (-1)^k + n*(2^(k + 1) + (-1)^k))/3.
%F A355668 G.f.: (x*(y-1) - y)/((x - 1)^2*(y + 1)*(2*y - 1)). - _Stefano Spezia_, Jul 13 2022
%e A355668 Row n=0 is A001045(k), then for further rows we successively add A001045(k+1).
%e A355668        k=0  k=2  k=3  k=4  k=5  k=6  k=7  k=8  k=9 k=10
%e A355668   n=0:  0    1    1    3    5   11   21   43   85  171 ... = A001045
%e A355668   n=1:  1    2    4    8   16   32   64  128  256  512 ... = A000079
%e A355668   n=2:  2    3    7   13   27   53  107  213  427  853 ... = A048573
%e A355668   n=3:  3    4   10   18   38   74  150  298  598 1194 ... = A171160
%e A355668   n=4:  4    5   13   23   49   95  193  383  769 1535 ... = abs(A140683)
%e A355668   ...
%t A355668 T[n_, k_] := (2^k - (-1)^k + n*(2^(k + 1) + (-1)^k))/3; Table[T[n - k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Jul 13 2022 *)
%Y A355668 Cf. A001477, A000027, A016777, A016885, A017449, A321373.
%Y A355668 Antidiagonal sums give A320933(n+1).
%K A355668 nonn,tabl,easy
%O A355668 0,4
%A A355668 _Paul Curtz_, Jul 13 2022