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A084152
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Exponential self-convolution of Jacobsthal numbers (divided by 2).
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4
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0, 0, 1, 3, 15, 55, 231, 903, 3655, 14535, 58311, 232903, 932295, 3727815, 14913991, 59650503, 238612935, 954429895, 3817763271, 15270965703, 61084037575, 244335800775, 977343902151, 3909374210503, 15637499638215, 62549992960455
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index to sequences with linear recurrences with constant coefficients, signature (3,6,-8).
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FORMULA
| a(n) = (4^n-2+(-2)^n)/18.
G.f.: x^2/((1-x)*(1+2*x)*(1-4*x)).
a(n) = +3*a(n-1) +6*a(n-2) -8*a(n-3).
E.g.f.: (exp(2*x)-exp(-x))^2/18 = (exp(4*x)-2*exp(x)+exp(-x))/18.
Binomial transform of 0, 0, 1, 0, 9, 0, 81, ... a(n)=A001045(n)*A078008(n)/2.
a(n) = floor(2^n/3)ceiling(2^n/3)/2 - Paul Barry, Apr 28 2004
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MATHEMATICA
| Join[{a=0, b=0}, Table[c=2*b+8*a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 05 2011*)
LinearRecurrence[{3, 6, -8}, {0, 0, 1}, 30] (* From Harvey P. Dale, Nov 11 2011 *)
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PROG
| (MAGMA) [(4^n-2+(-2)^n)/18: n in [0..35]]; // Vincenzo Librandi, Jul 05 2011
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CROSSREFS
| Cf. A001045, A084153.
Except for initial terms, same as A015249 and A084175.
Sequence in context: A007973 A015249 * A084175 A081951 A033853 A049187
Adjacent sequences: A084149 A084150 A084151 * A084153 A084154 A084155
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 16 2003
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