A166455 Triangle read by rows, twice Pascal's triangle minus Sierpinski's gasket: 2*A007318 - A047999.

1, 1, 1, 1, 4, 1, 1, 5, 5, 1, 1, 8, 12, 8, 1, 1, 9, 20, 20, 9, 1, 1, 12, 29, 40, 29, 12, 1, 1, 13, 41, 69, 69, 41, 13, 1, 1, 16, 56, 112, 140, 112, 56, 16, 1, 1, 17, 72, 168, 252, 252, 168, 72, 17, 1, 1, 20, 89, 240, 420, 504, 420, 240, 89, 20, 1, 1, 21, 109, 329, 660, 924, 924, 660, 329, 109, 21, 1

Offset

0,5

Links

Table of n, a(n) for n=0..77.

Example

First few rows of the triangle:
1;
1, 1;
1, 4, 1;
1, 5, 5, 1;
1, 8, 12, 8, 1;
1, 9, 20, 20, 9, 1;
1, 12, 29, 40, 29, 12, 1;
1, 13, 41, 69, 69, 41, 13, 1;
1, 16, 56, 112, 140, 112, 56, 16, 1;
1, 17, 72, 168, 252, 252, 168, 72, 17, 1;
1, 20, 89, 240, 420, 504, 420, 240, 89, 20, 1;
1, 21, 109, 329, 660, 924, 924, 660, 329, 109, 21, 1;
1, 24, 132, 440, 989, 1584, 1848, 1584, 989, 440, 132, 24, 1;
...

Mathematica

f[n_] := 2*n - Mod[n, 2]; T[n_, k_] := f[Binomial[n, k]]; Table[T[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Amiram Eldar, Aug 01 2023 *)

Crossrefs

Cf. A007318, A047999, A166456 (row sums).

Sequence in context: A143334 A156050 A136489 * A171142 A174037 A173077

Adjacent sequences: A166452 A166453 A166454 * A166456 A166457 A166458

Keyword

nonn,tabl

Author

Gary W. Adamson, Oct 14 2009

Extensions

a(26) = 12 inserted and more terms from Georg Fischer, Jun 07 2023

Status

approved