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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 (list; table; graph; refs; listen; history; text; internal format)
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 !! (n-2) !! (k-1)

a166454_row n = a166454_tabl !! (n-2)

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 A128651 A093797

Adjacent sequences:  A166451 A166452 A166453 * A166455 A166456 A166457

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Oct 14 2009

STATUS

approved

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Last modified December 12 20:04 EST 2017. Contains 295954 sequences.