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A075536
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a(n) = (1/2)((-1)^n+1)T(n)+(1/2)(-(-1)^n+1)S(n), where T(n) = tribonacci numbers A000073, S(n) = generalized tribonacci numbers A001644.
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1
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0, 1, 1, 7, 4, 21, 13, 71, 44, 241, 149, 815, 504, 2757, 1705, 9327, 5768, 31553, 19513, 106743, 66012, 361109, 223317, 1221623, 755476, 4132721, 2555757, 13980895, 8646064, 47297029, 29249425, 160004703, 98950096, 541292033, 334745777
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OFFSET
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0,4
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COMMENTS
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a(n)=T(n) if n even, a(n)=S(n) if n odd.
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LINKS
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Table of n, a(n) for n=0..34.
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FORMULA
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a(n)=3a(n-2)+a(n-4)+a(n-6), a(0)=0, a(1)=1, a(2)=1, a(3)=7, a(4)=4, a(5)=21. Ogf (x + x^2 + 4x^3 + x^4 - x^5)/(1 - 3x^2 - x^4 - x^6).
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MATHEMATICA
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CoefficientList[Series[(x+x^2+4x^3+x^4-x^5)/(1-3x^2-x^4-x^6), {x, 0, 40}], x]
LinearRecurrence[{0, 3, 0, 1, 0, 1}, {0, 1, 1, 7, 4, 21}, 40] (* Harvey P. Dale, Jul 10 2012 *)
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CROSSREFS
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Cf. A000073, A001644, A005013, A005247.
Sequence in context: A181138 A063632 A147601 * A085047 A213831 A213564
Adjacent sequences: A075533 A075534 A075535 * A075537 A075538 A075539
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KEYWORD
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easy,nonn
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AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Sep 23 2002
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STATUS
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approved
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