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

0,4

Links

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

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

Example

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)
  ...

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 *)

Crossrefs

Cf. A001477, A000027, A016777, A016885, A017449, A321373.

Antidiagonal sums give A320933(n+1).

Sequence in context: A200779 A286558 A368153 * A023990 A117894 A177762

Adjacent sequences: A355665 A355666 A355667 * A355669 A355670 A355671

Keyword

nonn,tabl,easy

Author

Paul Curtz, Jul 13 2022

Status

approved