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A001352
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a(0) = 1, a(1) = 6, a(2) = 24; for n>=3, a(n) = 4a(n-1) - a(n-2).
(Formerly M4164 N1731)
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3
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1, 6, 24, 90, 336, 1254, 4680, 17466, 65184, 243270, 907896, 3388314, 12645360, 47193126, 176127144, 657315450, 2453134656, 9155223174, 34167758040, 127515808986, 475895477904, 1776066102630, 6628368932616, 24737409627834
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Also the coordination sequence of a {4,6} tiling of the hyperbolic plane, where there are 6 squares (with vertex angles Pi/3) around every vertex. - toen (tca110(AT)rsphysse.anu.edu.au), May 16 2005
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REFERENCES
| T. N. E. Greville, Table for third-degree spline interpolations with equally spaced arguments, Math. Comp., 24 (1970), 179-.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
| g.f.: 1+6x/(1-4x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
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MAPLE
| A001352 := proc(n) coeftayl(1+6*x/(1-4*x+x^2), x=0, n) ; end: for n from 0 to 30 do printf("%d, ", A001352(n)) ; od ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
A001352:=(z+1)**2/(1-4*z+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
| Join[{1}, LinearRecurrence[{4, -1}, {6, 24}, 30]] (* From Harvey P. Dale, Jul 20 2011 *)
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CROSSREFS
| First differences of A082841. Pairwise sums of A001834.
Sequence in context: A181618 A002919 A006780 * A155602 A179716 A079839
Adjacent sequences: A001349 A001350 A001351 * A001353 A001354 A001355
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 06 2007
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