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Search: id:A117585
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| A117585 |
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a(n) = 2*(a(n-1))+ a(n-2) + n. |
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+0
1
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| 1, 3, 9, 24, 61, 151, 369, 896, 2169, 5243, 12665, 30584, 73845, 178287, 430433, 1039168, 2508785, 6056755, 14622313, 35301400, 85225133, 205751687, 496728529, 1199208768, 2895146089, 6989500971, 16874148057, 40737797112, 98349742309
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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A modified Pellian sequence.
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FORMULA
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a(n)/a(n-1) tends to 1 + sqrt(2) = 2.414213562...(a(14)/a(13) = 430433/178287 = 2.4142702...).
(1/2) [Pell(n+1) + 2*Pell(n) - n - 2 ], with Pell(n) = A000129(n). - Ralf Stephan, May 15 2007
a(n)=4*a(n-1)-4*a(n-2)+a(n-4). G.f.: -(1-x+x^2)/((x^2+2*x-1)*(x-1)^2). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2009]
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EXAMPLE
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a(4) = 61 = 2*(a(3)) + a(2) + 4 = 2*24 + 9 + 4.
a(4) = 61 = sum of terms in row 5 of A117584: 1 + 5 + 9 + 17 + 29.
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CROSSREFS
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Row sums of triangle A117584.
Sequence in context: A084858 A003262 A079282 this_sequence A006684 A018788 A098690
Adjacent sequences: A117582 A117583 A117584 this_sequence A117586 A117587 A117588
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 29 2006
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EXTENSIONS
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More terms from Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Jun 25 2009
Terms from a(20) on corrected by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 05 2009
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