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A107240
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Sum of squares of first n tribonacci numbers (A000213).
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3
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1, 2, 3, 12, 37, 118, 407, 1368, 4617, 15642, 52891, 178916, 605325, 2047726, 6927407, 23435376, 79281105, 268206130, 907335091, 3069492092, 10384017717, 35128880742, 118840150983, 402033352264, 1360069089113, 4601080768074
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) is prime for n = 2, 3, 5, 15, 29, ... a(n) is semiprime for n = 7, 11, 21, 33, ... For Fibonacci numbers (A000045) F(i) we have SUM[from i=1 to n]F(i) = F(n)*F(n+1).
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REFERENCES
| M. Feinberg, "Fibonacci-Tribonacci." Fib. Quart. 1, 71-74, 1963.
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LINKS
| Eric Weisstein's World of Mathematics, Tribonacci Number..
Harvey P. Dale, Table of n, a(n) for n = 1..1000
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FORMULA
| a(n) = SUM[from i=1 to n][A000213(i)]^2.
a(n)= 3*a(n-1) +a(n-2) +3*a(n-3) -7*a(n-4) +a(n-5) -a(n-6) +a(n-7). G.f.: (x^3-x^2+3*x-1)*(1+x)^2/((x-1)*(x^3+x^2+3*x-1)*(x^3-x^2-x-1)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 11 2009]
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EXAMPLE
| a(1) = 1^2 = 1.
a(2) = 1^2 + 1^2 = 1.
a(3) = 1^2 + 1^2 + 1^2 = 3, prime.
a(4) = 1^2 + 1^2 + 1^2 + 3^2 = 12.
a(5) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 = 37, prime.
a(6) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 + 9^2 = 118 = 2 * 59, semiprime.
a(7) = 1^2 + 1^2 + 1^2 + 3^2 + 5^2 + 9^2 + 17^2 = 407 = 11 * 37, semiprime.
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MATHEMATICA
| Accumulate[LinearRecurrence[{1, 1, 1}, {1, 1, 1}, 30]^2] (* From Harvey P. Dale, Nov 11 2011 *)
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CROSSREFS
| Cf. A000213, A107240, A107239-A107248.
Sequence in context: A165301 A072440 A135522 * A099171 A012307 A012311
Adjacent sequences: A107237 A107238 A107239 * A107241 A107242 A107243
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 14 2005
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