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A178616 Triangle by columns, odd columns of Pascal's triangle A007318, else (1, 0, 0, 0,...) 4
1, 0, 1, 0, 2, 1, 0, 3, 0, 1, 0, 4, 0, 4, 1, 0, 5, 0, 10, 0, 1, 0, 6, 0, 20, 0, 6, 1, 0, 7, 0, 35, 0, 21, 0, 1, 0, 8, 0, 56, 0, 56, 0, 8, 0, 1, 0, 9, 0, 84, 0, 126, 0, 36, 0, 1, 0, 10, 0, 120, 0, 252, 0, 120, 0, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums = a variant of A052950, starting (1, 1, 3, 4, 9, 16, 33,...); whereas

A052950 starts (2, 1, 3, 4, 9,...).

Column 1 of the inverse of A178616 is a signed variant of A065619 prefaced

with an 0; where A065619 = (1, 2, 3, 8, 25, 96, 427,...).

LINKS

Table of n, a(n) for n=0..66.

FORMULA

Triangle, odd columns of Pascal's triangle; (1, 0, 0, 0,...) as even columns k.

Alternatively, (since A178616 + A162169 - Identity matrix) = Pascal's triangle,

we can begin with Pascal's triangle, subtract A162169, then add the Identity

matrix to obtain A178616.

EXAMPLE

First few rows of the triangle =

1,

0, 1;

0, 2, 1;

0, 3, 0, 1

0, 4, 0, 4, 1;

0, 5, 0, 10, 0, 1;

0, 6, 0, 20, 0, 6, 1;

0, 7, 0, 35, 0, 21, 0, 1;

0, 8, 0, 56, 0, 56, 0 8, 1;

0, 9, 0, 84, 0, 126, 0, 36, 0, 1;

0, 10, 0, 120, 0, 252, 0, 120, 0, 10, 1;

0, 11, 0, 165, 0, 462, 0, 330, 0, 55, 0, 1;

...

CROSSREFS

Cf. A162109, A065619, A052950, A095704.

Sequence in context: A159813 A157409 A245960 * A165252 A127373 A200123

Adjacent sequences:  A178613 A178614 A178615 * A178617 A178618 A178619

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, May 30 2010

STATUS

approved

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Last modified August 10 22:22 EDT 2020. Contains 336403 sequences. (Running on oeis4.)