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A127985
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Numbers of the form (n/3 + 4/9)*2^(n) - 1/2 + (-1)^n/18.
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1
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1, 4, 11, 28, 67, 156, 355, 796, 1763, 3868, 8419, 18204, 39139, 83740, 178403, 378652, 800995, 1689372, 3553507, 7456540, 15612131, 32622364, 68040931, 141674268, 294533347, 611436316, 1267611875, 2624702236, 5428361443
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Wieb Bosma, Signed bits and fast exponentiation, J. Th. des Nombres de Bordeaux, vol. 13, fasc. 1, pp. 27-41, 2001.
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FORMULA
| a(n) = (n/3 + 4/9)*2^(n) - 1/2 + (-1)^n/18
a(0)=1, a(1)=4, a(2)=11, a(3)=28, a(n)=4*a(n-1)-3*a(n-2)-4*a(n-3)+4*a(n-4) [From Harvey P. Dale, May 15 2011]
G.f.: x*(1-2*x^2)/((1-2*x)^2*(1-x^2)) [From Harvey P. Dale, May 15 2011]
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MATHEMATICA
| Table[(n/3 + 4/9)2^(n) - 1/2 + (-1)^n/18, {n, 1, 50}] (* Artur Jasinski *)
LinearRecurrence[{4, -3, -4, 4}, {1, 4, 11, 28}, 50] (* From Harvey P. Dale, May 15 2011 *)
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PROG
| (MAGMA) [(n/3 + 4/9)*2^(n) - 1/2 + (-1)^n/18: n in [1..40]]; // Vincenzo Librandi, May 26 2011
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CROSSREFS
| Cf. A073371, A127976, A127978, A127979, A127980, A127981, A127982, A127983, A127984, A073371, A000337.
Sequence in context: A056601 A003230 A099326 * A005409 A020964 A113067
Adjacent sequences: A127982 A127983 A127984 * A127986 A127987 A127988
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007
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