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A123011 a(n) = 2*a(n-1)+5*a(n-2) 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^(n-1) times the sum of the two elements in the top row of the n-th 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+(3-2*sqrt(6))*(1-sqrt(6))^n)/6. - Klaus Brockhaus, Aug 15 2009

G.f.: (1+3*x)/(1-2*x-5*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*n-3 else 2*Self(n-1)+5*Self(n-2): 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

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Last modified April 21 21:03 EDT 2018. Contains 302877 sequences. (Running on oeis4.)