|
Search: id:A113071
|
|
|
| A113071 |
|
Expansion of ((1+x)/(1-3x))^2. |
|
+0
3
|
|
| 1, 8, 40, 168, 648, 2376, 8424, 29160, 99144, 332424, 1102248, 3621672, 11809800, 38263752, 123294312, 395392104, 1262703816, 4017693960, 12741829416, 40291730856, 127073920392, 399817944648, 1255242384360, 3933092804328
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
Binomial transform is A014916. In general, ((1+x)/(1-r*x))^2 expands to a(n)=((r+1)r^n((r+1)n+r-1)+0^n)/r^2, which is also a(n)=sum{k=0..n, C(n,k)*sum{j=0..k, (j+1)*(r+1)^j}}. This is the self-convolution of the coordination sequence for the infinite tree with valency r.
|
|
FORMULA
|
G.f.: (1+x^2)/(1-3x)^2; a(n)=8*3^n(2n+1)/9+0^n/9=4*3^n(4n+2)/9+0^n/9; a(n)=sum{k=0..n, A003946(k)A003946(n-k)}; a(n)=sum{k=0..n, C(n, k)*sum{j=0..k, (j+1)*4^j}}.
|
|
CROSSREFS
|
Sequence in context: A004405 A001789 A074412 this_sequence A006726 A165665 A000760
Adjacent sequences: A113068 A113069 A113070 this_sequence A113072 A113073 A113074
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Oct 14 2005
|
|
|
Search completed in 0.002 seconds
|
