

A123011


a(n) = 2*a(n1)+5*a(n2) for n > 1; a(0) = 1, a(1) = 5.


3



1, 5, 15, 55, 185, 645, 2215, 7655, 26385, 91045, 314015, 1083255, 3736585, 12889445, 44461815, 153370855, 529050785, 1824955845, 6295165615, 21715110455, 74906048985, 258387650245, 891305545415, 3074549342055
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


COMMENTS

a(n) is also 5^(n1) times the sum of the two elements in the top row of the nth power of the symmetric matrix (0,1; 1/5,2/5).  see Mathematica code.


LINKS

Table of n, a(n) for n=0..23.


FORMULA

a(n) = ((3+2*sqrt(6))*(1+sqrt(6))^n+(32*sqrt(6))*(1sqrt(6))^n)/6.  Klaus Brockhaus, Aug 15 2009
G.f.: (1+3*x)/(12*x5*x^2).  Klaus Brockhaus, Aug 15 2009
Binomial transform of A164532. Inverse binomial transform of A164549.  Klaus Brockhaus, Aug 15 2009


MATHEMATICA

M := {{0, 1}, {1/5, 2/5}}; v[1] = {1, 1}; v[n_] := v[n] = M.v[n  1]; a = Table[v[n][[1]]*5^(n  1), {n, 1, 30}]


PROG

(MAGMA) [ n le 2 select 4*n3 else 2*Self(n1)+5*Self(n2): n in [1..24] ];  Klaus Brockhaus, Aug 15 2009


CROSSREFS

Cf. A164532, A164549.
Sequence in context: A243076 A002221 A007714 * A006358 A054108 A149585
Adjacent sequences: A123008 A123009 A123010 * A123012 A123013 A123014


KEYWORD

nonn


AUTHOR

Roger L. Bagula, Sep 23 2006


EXTENSIONS

Edited by N. J. A. Sloane, Aug 27 2009, using simpler definition suggested by Klaus Brockhaus, Aug 15 2009


STATUS

approved



