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Search: id:A107239
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| 0, 0, 1, 2, 6, 22, 71, 240, 816, 2752, 9313, 31514, 106590, 360606, 1219935, 4126960, 13961456, 47231280, 159782161, 540539330, 1828631430, 6186215574, 20927817799, 70798300288, 239508933824, 810252920400, 2741065994769
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OFFSET
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0,4
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COMMENT
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Not to be confused with A107240 which is based on alternate tribonacci sequence A000213(n), which starts 1,1,1,3. Prime values include: a(4) = 2, a(7) = 71. Semiprime values include: a(5) = 6 = 2 * 3, a(6) = 22 = 2 * 11, a(11) = 9313 = 67 * 139, a(35) = 3 * 15674342521439179.
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REFERENCES
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M. Feinberg, "Fibonacci-Tribonacci." Fib. Quart. 1, 71-74, 1963.
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LINKS
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Eric Weisstein's World of Mathematics, Tribonacci Number..
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FORMULA
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a(n) = T(1)^2 + T(2)^2 + ... T(n)^2 where T(n) = A000073(n). a(0) = 0 and a(n+1) = a(n) + A000073(n+1).
a(n)=sum(i=0..n-2) A085697(i). G.f.: x^2*(1-x-x^2-x^3)/((x^3-x^2-x-1)(x^3+x^2+3*x-1)(1-x)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 19 2008]
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EXAMPLE
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a(1) = 0 = 0^2
a(2) = 0 = 0^2 + 0^2
a(3) = 1 = 0^2 + 0^2 + 1^2
a(4) = 2 = 0^2 + 0^2 + 1^2 + 1^2
a(5) = 6 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2
a(6) = 22 = 0^2 + 0^2 + 1^2 + 1^1 + 2^2 + 4^2
a(7) = 71 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 + 7^2
a(8) = 240 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 + 7^2 + 13^2
a(9) = 816 = 0^2 + 0^2 + 1^2 + 1^2 + 2^2 + 4^2 + 7^2 + 13^2 + 24^2
a(10) = 2752 = 44^2 + 816
a(11) = 9313 = 81^2 + 2752
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CROSSREFS
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Cf. A000073, A000213, A107240, A107241-A107248.
Sequence in context: A002839 A109194 A014334 this_sequence A148496 A106434 A150228
Adjacent sequences: A107236 A107237 A107238 this_sequence A107240 A107241 A107242
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 17 2005
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