

A131061


Triangle read by rows: T(n,k)=4*binom(n,k)3 (0<=k<=n).


10



1, 1, 1, 1, 5, 1, 1, 9, 9, 1, 1, 13, 21, 13, 1, 1, 17, 37, 37, 17, 1, 1, 21, 57, 77, 57, 21, 1, 1, 25, 81, 137, 137, 81, 25, 1, 1, 29, 109, 221, 277, 221, 109, 29, 1, 1, 33, 141, 333, 501, 501, 333, 141, 33, 1, 1, 37, 177, 477, 837, 1005, 837, 477, 177, 37, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


COMMENTS

Row sums = A131062: (1, 2, 7, 20, 49, 110, 235,...); the binomial transform of (1, 1, 4, 4, 4,...).
4*A007318  3*A000012 as infinite lower triangular matrices.  Emeric Deutsch, Jun 21 2007


LINKS

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


FORMULA

G.f.=G(t,z)=(1ztz+4tz^2)/[(1z)(1tz)(1ztz)].  Emeric Deutsch, Jun 21 2007


EXAMPLE

First few rows of the triangle are:
1;
1, 1;
1, 5, 1;
1, 9, 9, 1;
1, 13, 21, 13, 1;
1, 17, 37, 37, 17, 1;
1, 21, 57, 77, 57, 21, 1;
...


MAPLE

T := proc (n, k) if k <= n then 4*binomial(n, k)3 else 0 end if end proc; for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form  Emeric Deutsch, Jun 21 2007


CROSSREFS

Cf. A131060, A131062, A131063, A131064, A131065, A131066.
Sequence in context: A153108 A157174 A183450 * A157169 A081578 A184883
Adjacent sequences: A131058 A131059 A131060 * A131062 A131063 A131064


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Jun 13 2007


EXTENSIONS

More terms from Emeric Deutsch, Jun 21 2007


STATUS

approved



