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A159612
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INVERT transform of (1, 3, 1, 3, 1,...)
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14
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1, 4, 8, 24, 56, 152, 376, 984, 2488, 6424, 16376, 42072, 107576, 275864, 706168, 1809624, 4634296, 11872792, 30409976, 77901144, 199541048, 511145624, 1309309816, 3353892312, 8591131576, 22006700824, 56371227128, 144398030424, 369882938936, 947475060632, 2427006816376
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| The sequence 1,1,4,8,24,... is an eigensequence of the sequence triangle of 1,3,1,3,1,3,1,..., which is the Riordan array ((1+3x)/(1-x^2),x). [Paul Barry, Feb 10 2011]
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FORMULA
| G.f.: (1-x^2)/(1-x-4*x^2) = 1/(1-x*(1+3*x)/(1-x^2)).
a(n) = a(n-1) + 4*a(n-2), a(1)=1, a(2)=4. - Vincenzo Librandi, Mar 11 2011
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EXAMPLE
| a(4) = 24 = (1, 3, 1, 3) dot (8, 4, 1, 1) = (8 + 12, + 1 + 3).
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MATHEMATICA
| LinearRecurrence[{1, 4}, {1, 4}, 50] (* From Vladimir Joseph Stephan Orlovsky, Jul 17 2011 *)
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CROSSREFS
| Sequence in context: A180002 A115641 A153334 * A099176 A190156 A116556
Adjacent sequences: A159609 A159610 A159611 * A159613 A159614 A159615
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 17 2009
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