login
Binomial transform of [1, 0, 0, 4, 0, 0, 7, 0, 0, 10, ...].
0

%I #9 Feb 08 2019 08:29:09

%S 1,1,1,5,17,41,88,190,421,935,2051,4445,9562,20476,43681,92837,196613,

%T 415073,873820,1835002,3844765,8039075,16777223,34952549,72701278,

%U 150994936,313174681,648719009,1342177289,2773833065,5726623072

%N Binomial transform of [1, 0, 0, 4, 0, 0, 7, 0, 0, 10, ...].

%F A007318 * [1, 0, 0, 4, 0, 0, 7, 0, 0, 10, ...].

%F a(n) = Sum_{k=0..n/3} (3k+1)*binomial(n,3k). - _Emeric Deutsch_, May 03 2008

%F G.f.: x*(1 - 3x + 3x^2 + x^3)*(1-x)^2/((1-2x)^2*(1-x+x^2)^2). - _R. J. Mathar_, Nov 25 2008

%e a(4) = 5 = (1, 3, 3, 1) dot (1, 0, 0, 4) = (1 + 0 + 0 + 4).

%p a:=proc(n) options operator, arrow: sum((3*k+1)*binomial(n,3*k),k=0..(1/3)*n) end proc: seq(a(n),n=0..30); # _Emeric Deutsch_, May 03 2008

%K nonn

%O 1,4

%A _Gary W. Adamson_, Apr 26 2008

%E More terms from _Emeric Deutsch_, May 03 2008