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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 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 December 13 16:00 EST 2018. Contains 318086 sequences. (Running on oeis4.)