A179135 a(n) = (3-sqrt(5))*((3+sqrt(5))/10)^(-n)/2+(3+sqrt(5))*((3-sqrt(5))/10)^(-n)/2.

3, 35, 450, 5875, 76875, 1006250, 13171875, 172421875, 2257031250, 29544921875, 386748046875, 5062597656250, 66270263671875, 867489013671875, 11355578613281250, 148646453857421875, 1945807342529296875

Offset: 0

Author

Johannes W. Meijer, Jul 01 2010

Keywords

• easy
• nonn

Links

• Index entries for linear recurrences with constant coefficients, signature (15, -25).

Crossrefs

Cf. A109106.

Programs

Maple

with(GraphTheory): nmax:=72; P:=9: G:=PathGraph(P): A:= AdjacencyMatrix(G): for n from 0 to nmax do B(n):=A^n; A178381(n):=add(B(n)[1,k],k=1..P); od: for n from 0 to nmax/4-1 do a(n):= A178381(4*n+3) od: seq(a(n),n=0..nmax/4-1);

Formula

a(n) = A178381(4*n+3).

G.f.: (3-10*z)/(1-15*z+25*z^2).

Limit(a(n+k)/a(k), k=infinity) = A000351(n)*A130196(n)/(A128052(n) - A167808(2*n)*sqrt(5)).

Limit(A128052(n)/A167808(2*n),n=infinity) = sqrt(5).

a(n) = 5^n*Lucas(2*(n+1)). - Ehren Metcalfe, Apr 22 2018