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A107767
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a(n)=(1+3^n-2*3^(n/2))/4 if n even; a(n)=(1+3^n-4*3^((n-1)/2))/4 if n odd.
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1
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0, 1, 4, 16, 52, 169, 520, 1600, 4840, 14641, 44044, 132496, 397852, 1194649, 3585040, 10758400, 32278480, 96845281, 290545684, 871666576, 2615029252, 7845176329, 23535617560, 70607118400, 211821620920, 635465659921
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| Gy. Tasi and F. Mizukami, Quantum algebraic-combinatoric study of the conformational properties of n-alkanes, J. Math. Chemistry, 25, 1999, 55-64 (see p. 60).
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (4,0,-12,9).
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FORMULA
| G.f.: -x^2 / ( (x-1)*(3*x-1)*(3*x^2-1) ). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 16 2010
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MAPLE
| a:=proc(n) if n mod 2 = 0 then (1+3^n-2*3^(n/2))/4 else (1+3^n-4*3^((n-1)/2))/4 fi end: seq(a(n), n=1..32);
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CROSSREFS
| Cf. A167993 (first differences).
Sequence in context: A007688 A197132 A100774 * A087972 A074409 A056589
Adjacent sequences: A107764 A107765 A107766 * A107768 A107769 A107770
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KEYWORD
| nonn
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AUTHOR
| Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 12 2005
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EXTENSIONS
| Entry revised by N. J. A. Sloane, Jul 29 2011
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