A321373 Array T(n,k) read by antidiagonals where the first row is (-1)^k*A140966(k) and each subsequent row is obtained by adding A001045(k) to the preceding one.

2, 2, -1, 2, 0, 3, 2, 1, 4, 1, 2, 2, 5, 4, 7, 2, 3, 6, 7, 12, 9, 2, 4, 7, 10, 17, 20, 23, 2, 5, 8, 13, 22, 31, 44, 41, 2, 6, 9, 16, 27, 42, 65, 84, 87, 2, 7, 10, 19, 32, 53, 86, 127, 172, 169, 2, 8, 11, 22, 37, 64, 107, 170, 257, 340, 343

Offset

0,1

Comments

Array:

2, -1, 3, 1, 7, 9, 23, 41, 87, ... = (-1)^n*A140966(n)

2, 0, 4, 4, 12, 20, 44, 84, 172, ... = abs(A084247(n+1))

2, 1, 5, 7, 17, 31, 65, 127, 257, ... = A014551(n)

2, 2, 6, 10, 22, 42, 86, 170, 342, ... = A078008(n+2) = A014113(n+1)

2, 3, 7, 13, 27, 53, 107, 213, 427, ... = A048573(n)

2, 4, 8, 16, 32, 64, 128, 256, 512, ... = A000079(n+1)

2, 5, 9, 19, 37, 75, 149, 299, 597, ... = A062092(n)

2, 6, 10, 22, 42, 86, 170, 342, 682, ... = A078008(n+3) = A014113(n+2).

T(n+1,k) = (-1)^k *A140996(k) + (n+1)*A001045(k).

Every row T(n+1,k) has the signature (1,2).

T(0,k) = 2, -2, 2, -2, ... = (-1)^n*2.

T(n+1,k) - T(0,k) = (n+1)*A001045(n).

5*A001045(n) is not in the OEIS.

Links

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

Example

Triangle a(n):
  2;
  2, -1;
  2,  0,  3;
  2,  1,  4,  1;
  2,  2,  5,  4,  7;
  2,  3,  6,  7, 12,  9;
  2,  4,  7, 10, 17, 20, 23;
  etc.
Row sums: 2, 1, 5, 8, 20, 39, 83, 166, 338, 677, 1361, 2724, ... = b(n+2).
With b(0) = 2 and b(1) = 0, b(n) = b(n-1) + 2*b(n-2)  + n - 4, n > 1.
b(n) = A001045(n) - A097065(n-1).
b(n) = b(n-2) + A000225(n-2).

Mathematica

T[_, 0] = 2;
T[0, k_] := (2^k + 5(-1)^k)/3;
T[n_ /; n>0, k_ /; k>0] := T[n, k] = T[n-1, k] + (2^k + (-1)^(k+1))/3;
T[_, _] = 0;
Table[T[n-k, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 10 2018 *)

Crossrefs

Cf. A000079, A001045, A014113, A014551, A048573, A062092, A078008, A084247, A092297, A097073, A140360, A140966.

Cf. A000225, A097065.

Sequence in context: A225064 A361967 A130071 * A305615 A038540 A335060

Adjacent sequences: A321370 A321371 A321372 * A321374 A321375 A321376

Keyword

sign,tabl

Author

Paul Curtz, Nov 08 2018

Status

approved