

A166454


Triangle read by rows, (1/2)*(Pascal's triangle  Sierpinski's gasket); (1/2)*(A007318  A047999).


5



1, 1, 1, 2, 3, 2, 2, 5, 5, 2, 3, 7, 10, 7, 3, 3, 10, 17, 17, 10, 3, 4, 14, 28, 35, 28, 14, 4, 4, 18, 42, 63, 63, 42, 18, 4, 5, 22, 60, 105, 126, 105, 60, 22, 5, 5, 27, 82, 165, 231, 231, 165, 82, 27, 5
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OFFSET

2,4


COMMENTS

Row sums = A120739: (1, 2, 7, 14, 30, 60, 127, 254,...).


LINKS

Reinhard Zumkeller, Rows n = 2..125 of triangle, flattened


FORMULA

(1/2)*(A007318  A047999), nonzero terms.
t(n,m) = Floor[Binomial[n, m]/2] [From Roger L. Bagula, Mar 07 2010]


EXAMPLE

First few rows of the triangle =
1;
1, 1;
2, 3, 2;
2, 5, 5, 2;
3, 7, 10, 7, 3;
3, 10, 17, 17, 10, 3;
4, 14, 28, 35, 28, 14, 4;
4, 18, 42, 63, 63, 42, 18, 4;
5, 22, 60, 105, 126, 105, 60, 22, 5;
5, 27, 82, 165, 231, 231, 165, 82, 27, 5;
6, 33, 110, 247, 396, 462, 396, 247, 110, 33, 6;
...


MATHEMATICA

Contribution from Roger L. Bagula, Mar 07 2010: (Start)
Clear[t, n, m];
t[n_, m_] = Floor[Binomial[n, m]/2];
Table[Table[t[n, m], {m, 1, n  1}], {n, 2, 12}];
Flatten[%] (End)


PROG

(Haskell) Following Bagula's formula
a166454 n k = a166454_tabl !! (n2) !! (k1)
a166454_row n = a166454_tabl !! (n2)
a166454_tabl = map (map (flip div 2) . init . tail) $ drop 2 a007318_tabl
 Reinhard Zumkeller, Mar 04 2015


CROSSREFS

A047999, A120739.
Cf. A007318, A011848, A001700 (central terms).
Sequence in context: A027746 A240230 A238689 * A283239 A318177 A128651
Adjacent sequences: A166451 A166452 A166453 * A166455 A166456 A166457


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Oct 14 2009


STATUS

approved



