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Search: id:A166517
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| A166517 |
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a(n)=3*n-a(n-1), with a(1)=1. |
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+0
2
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| 1, 5, 4, 8, 7, 11, 10, 14, 13, 17, 16, 20, 19, 23, 22, 26, 25, 29, 28, 32, 31, 35, 34, 38, 37, 41, 40, 44, 43, 47, 46, 50, 49, 53, 52, 56, 55, 59, 58, 62, 61, 65, 64, 68, 67, 71, 70, 74, 73, 77, 76, 80, 79, 83, 82, 86, 85, 89, 88, 92, 91, 95, 94, 98, 97, 101, 100, 104, 103, 107
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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A sequence defined by a(1)=1, a(n)=k*n-a(n-1), k a constant parameter, has recurrence a(n)= 3*a(n-1) -3*a(n-2) +a(n-3). Its generating function is x*(1+2*(k-1)*x+(1-k)*x^2)/((1+x)*(1-x)^2). The closed form is a(n) = k*n/2+k/4+(-1)^n*(3*k/4-1). This applies with k=3 to this sequence here, and for example to sequences A165033, and A166519-A166525. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 17 2009]
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EXAMPLE
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For n=2, a(2)=3*2-1=5; n=3, a(3)=3*3-5=4; n=4, a(4)=3*4-4=8; n=5, a(5)=7
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CROSSREFS
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Sequence in context: A065015 A002340 A023845 this_sequence A051555 A086407 A160427
Adjacent sequences: A166514 A166515 A166516 this_sequence A166518 A166519 A166520
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Oct 16 2009
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