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Search: id:A113301
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| A113301 |
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Sum of odd-indexed terms of tribonacci numbers. |
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+0
2
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| 0, 1, 5, 18, 62, 211, 715, 2420, 8188, 27701, 93713, 317030, 1072506, 3628263, 12274327, 41523752, 140473848, 475219625
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A000073 is the tribonacci numbers. A113300 is the sum of even-indexed terms of tribonacci numbers. A099463 is the bisection of the tribonacci numbers. A113300(n) + A113301(n) = cumulative sum of tribonacci numbers = A008937(n). Primes in A113300 include a(2) = 5, a(5) = 211, a(9) = 27701, .... A113300 is semiprime for n = 4, 10, 14, ...
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FORMULA
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a(n) = sum[from i = 0 to n] A000073(2*n+1). A113300(n) + A113301(n) = A008937(n).
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EXAMPLE
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a(0) = 0 = A000073(1)
a(1) = 0+1 = A000073(1) + A000073(3) = 1;
a(2) = 0+1+4 = A000073(1) + A000073(3) + A000073(5) = 5, prime;
a(3) = 0+1+4+13 = A000073(1) + A000073(3) + A000073(5) + A000073(7) = 18;
a(4) = 0+1+4+13+44 = A000073(1) + A000073(3) + A000073(5) + A000073(7) + A000073(9) = 62 = 2 * 31, semiprime;
a(5) = 0+1+4+13+44+149 = A000073(1) + A000073(3) + A000073(5) + A000073(7) + A000073(9) + A000073(11) = 211, prime.
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CROSSREFS
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Cf. A000073, A008937, A099463, A113300.
Sequence in context: A104630 A062809 A122234 this_sequence A111567 A029869 A033453
Adjacent sequences: A113298 A113299 A113300 this_sequence A113302 A113303 A113304
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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), Oct 24 2005
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