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A139763
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a(n)=a(n-1)+a(n-2)+a(n-3)+2a(n-4) with a(n)=n+1 for n<=3.
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2
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1, 2, 3, 4, 11, 22, 43, 84, 171, 342, 683, 1364, 2731, 5462, 10923, 21844, 43691, 87382, 174763, 349524, 699051, 1398102, 2796203, 5592404, 11184811, 22369622
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,1,1,2)
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FORMULA
| a(n+1)-2a(n)=period 4:repeat 0, -1, -2, 3.
O.g.f.: (x-1)*(2*x^2+2*x+1)/((2*x-1)(1+x)(x^2+1)). a(n) = A056594(n+3)+((-1)^n+2^(n+1))/3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 22 2008
a(n)=2*a(n-1)+(1/4)*{-5*(n mod 4)+[(n+1) mod 4]+[(n+2) mod 4]+3*[(n+3) mod 4]}, a(0)=1 and n>=1 - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 03 2008
a(n)=-(1/2*I)*I^n+(1/3)*(-1)^n+(2/3)*2^n+(1/2*I)*(-I)^n, with n>=0 and I=(-1)^(1/2) - Paolo P. Lava (paoloplava(AT)gmail.com), Jun 03 2008
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CROSSREFS
| Sequence in context: A104109 A066347 A118596 * A037396 A037432 A116054
Adjacent sequences: A139760 A139761 A139762 * A139764 A139765 A139766
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KEYWORD
| nonn
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AUTHOR
| Paul Curtz (bpcrtz(AT)free.fr), May 20 2008
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 22 2008
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