A355668 Array read by upwards antidiagonals T(n,k) = J(k) + n*J(k+1) where J(n) = A001045(n) is the Jacobsthal numbers.
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, 16, 23, 38, 53, 64, 43, 8, 8, 19, 28, 49, 74, 107, 128, 85, 9, 9, 22, 33, 60, 95, 150, 213, 256, 171, 10, 10, 25, 38, 71, 116, 193, 298, 427, 512, 341
Offset: 0
Examples
Row n=0 is A001045(k), then for further rows we successively add A001045(k+1).
k=0 k=2 k=3 k=4 k=5 k=6 k=7 k=8 k=9 k=10
n=0: 0 1 1 3 5 11 21 43 85 171 ... = A001045
n=1: 1 2 4 8 16 32 64 128 256 512 ... = A000079
n=2: 2 3 7 13 27 53 107 213 427 853 ... = A048573
n=3: 3 4 10 18 38 74 150 298 598 1194 ... = A171160
n=4: 4 5 13 23 49 95 193 383 769 1535 ... = abs(A140683)
...
Crossrefs
Programs
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Mathematica
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 *)
Formula
T(n, k) = (2^k - (-1)^k + n*(2^(k + 1) + (-1)^k))/3.
G.f.: (x*(y-1) - y)/((x - 1)^2*(y + 1)*(2*y - 1)). - Stefano Spezia, Jul 13 2022