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0, 1, 2, -1, -12, -19, 22, 139, 168, -359, -1558, -1321, 5148, 16901, 8062, -68381, -177072, -12239, 860882, 1782959, -738492, -10391779, -17091098, 17776699, 121008888, 153134281, -298775878, -1363223161, -1232566932
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Partial sums of A006495. - Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index to sequences with linear recurrences with constant coefficients, signature (2,-5).
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FORMULA
| Contribution from Paul Barry (pbarry(AT)wit.ie), Sep 20 2003: (Start)
G.f.: x/(1-2x+5x^2);
E.g.f.: exp(x)sin(2x)/2;
a(n) = 2*a(n-1)-5*a(n-2), a(0)=0, a(1)=1;
a(n) = ((1+2i)^n-(1-2i)^n)/(4i), where i=sqrt(-1);
a(n) = Im{(1+2i)^n/2};
a(n) = sum{k=0..floor(n/2), C(n, 2k+1)(-4)^k}. (End)
a(n+1) = sum{k=0..n, C(k,n-k)2^k*(-5/2)^(n-k)}. - Paul Barry (pbarry(AT)wit.ie), Mar 16 2006
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=2*b-5*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 17 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 2, 5) for n in xrange(0, 29)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
(PARI) concat(0, Vec(1/(1-2*x+5*x^2)+O(x^99))) \\ Charles R Greathouse IV, Dec 22 2011
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CROSSREFS
| Cf. A084102, A088136, A088137, A088139.
a(n)^2 = A094423(n).
Sequence in context: A151508 A164826 A055392 * A110060 A061081 A007368
Adjacent sequences: A045870 A045871 A045872 * A045874 A045875 A045876
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KEYWORD
| sign,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Paul Barry (pbarry(AT)wit.ie), Sep 20 2003
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