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Search: id:A152733
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| A152733 |
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a(n)+a(n+1)+a(n+2)=3^n. |
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+0
2
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| 0, 0, 3, 6, 18, 57, 168, 504, 1515, 4542, 13626, 40881, 122640, 367920, 1103763, 3311286, 9933858, 29801577, 89404728, 268214184, 804642555, 2413927662, 7241782986, 21725348961, 65176046880, 195528140640, 586584421923
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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0+0+3=3^1;0+3+6=3^2;3+6+18=3^3;...
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FORMULA
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a(n)=3*A077834(n-3). G.f.: 3x^3/((1-3x)(1+x+x^2)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 12 2008]
a(n)=(1/13)*(3^n + 12*Cos[(2*n*Pi)/3] + 2*Sqrt[3]*Sin[(2*n*Pi)/3]), n=1,2,.. [From Zak Seidov (zakseidov(AT)yahoo.com), Dec 12 2008]
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MATHEMATICA
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k0=k1=0; lst={k0, k1}; Do[kt=k1; k1=3^n-k1-k0; k0=kt; AppendTo[lst, k1], {n, 1, 5!}]; lst
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CROSSREFS
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Cf. A152728,A152729,A152730,A152731,A152732,A152725,A152726,A000212
Sequence in context: A089325 A110593 A049368 this_sequence A102962 A076510 A038060
Adjacent sequences: A152730 A152731 A152732 this_sequence A152734 A152735 A152736
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KEYWORD
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nonn
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AUTHOR
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Vladimir Orlovsky (4vladimir(AT)gmail.com), Dec 11 2008
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