|
|
A073388
|
|
Convolution of A002605(n) (generalized (2,2)-Fibonacci), n >= 0, with itself.
|
|
8
|
|
|
1, 4, 16, 56, 188, 608, 1920, 5952, 18192, 54976, 164608, 489088, 1443776, 4238336, 12382208, 36022272, 104407296, 301618176, 868765696, 2495715328, 7152286720, 20452548608, 58369409024
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{k=0..n} b(k)*b(n-k), with b(k) = A002605(k).
a(n) = Sum_{k=0..floor(n/2)} binomial(n-k+1, 1)*binomial(n-k, k)*2^(n-k).
a(n) = ((n+1)*U(n+1) + 2*(n+2)*U(n))/6, with U(n) = A002605(n), n >= 0.
G.f.: 1/(1-2*x*(1+x))^2.
a(n) = Sum_{k=0..floor((n+2)/2)} k*binomial(n-k+2, k)2^(n-k+1). - Paul Barry, Oct 15 2004
|
|
MATHEMATICA
|
CoefficientList[Series[1/(1-2*x-2*x^2)^2, {x, 0, 40}], x] (* G. C. Greubel, Oct 03 2022 *)
|
|
PROG
|
(GAP) List([0..25], n->2^n*Sum([0..Int(n/2)], k->Binomial(n-k+1, 1)*Binomial(n-k, k)*(1/2)^k)); # Muniru A Asiru, Jun 12 2018
(Magma) R<x>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( 1/(1-2*x-2*x^2)^2 )); // G. C. Greubel, Oct 03 2022
|
|
CROSSREFS
|
Second (m=1) column of triangle A073387.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|