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A079162
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a(n) = 5a(n-2) - 2a(n-4).
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1
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0, 1, 2, 4, 10, 18, 46, 82, 210, 374, 958, 1706, 4370, 7782, 19934, 35498, 90930, 161926, 414782, 738634, 1892050, 3369318, 8630686, 15369322, 39369330, 70107974, 179585278, 319801226, 819187730, 1458790182, 3736768094
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| Also a(n) = a(n-1) + 2a(n-2) if n is odd, else a(n) = 2a(n-1) + a(n-2).
a(2n) = 2*A005824(2n), a(2n+1) = A005824(2n) + A005824(2n+1).
G.f.: x*(1+2*x-x^2)/(1-5*x^2+2*x^4).
a(n)=(1/68) * (-1)^n * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^(1/2) * n * sqrt(17)-(1/68) * [5/2-(1/2) * sqrt(17)]^(-1/4) * (-1)^n * sqrt(17) * [5/2 -(1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^(1/ 2) * n + (1/4) * [5/2-(1/2) * sqrt(17)]^( -1/4) * [5/2-(1/2) * sqrt(17)]^[(1/ 4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^(1/2) * n + (1/4) * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^(1/2) * n-(1/4) * (-1)^n * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^[(1/2) * n]-(1/4) * [5/2-(1/2) * sqrt(17)]^(-1/ 4) * (-1)^n * [5/2-(1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^(1/2) * n + (7/68) * [5/2 + (1/2) * sqrt(17)]^(-1/4) * [5/2 + (1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2 + (1/2) * sqrt(17)]^(1/ 2) * n * sqrt(17)-(7/68) * [5/2-(1/2) * sqrt(17)]^(-1/4) * sqrt(17) * [5/2-(1/2) * sqrt(17)]^[(1/4) * (-1)^n] * [5/2-(1/2) * sqrt(17)]^[(1 /2) * n], with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 06 2008]
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MATHEMATICA
| a[0] = 0; a[1] = 1; a[n_] := a[n] = If[ OddQ[n], a[n - 1] + 2a[n - 2], 2a[n - 1] + a[n - 2]]; Table[a[n], {n, 0, 30}]
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CROSSREFS
| Cf. A005824. a(2n+1) = A052913(n).
Sequence in context: A197049 A104723 A206140 * A197926 A043330 A011963
Adjacent sequences: A079159 A079160 A079161 * A079163 A079164 A079165
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KEYWORD
| nonn
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AUTHOR
| Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 29 2002
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EXTENSIONS
| Corrected the g.f. and index in formula with A052913 R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 01 2009, May 02 2009
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