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Search: id:A085903
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| A085903 |
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G.f.: (1 + 2x^2)/[(1+x)(1-2x)(1-2x^2)]. |
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+0
3
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| 1, 1, 7, 9, 31, 49, 127, 225, 511, 961, 2047, 3969, 8191, 16129, 32767, 65025, 131071, 261121, 524287, 1046529, 2097151, 4190209, 8388607, 16769025, 33554431, 67092481, 134217727, 268402689, 536870911, 1073676289, 2147483647
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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Resultant of the polynomial x^n-1 and the Chebyshev polynomial of the first kind T_2(x).
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FORMULA
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a(2n) = 2*4^n-1, a(2n+1) = (2^n-1)^2; interlaces A083420 with A060867 (squares of Mersenne numbers A000225). - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), May 19 2005
A107663(2n) = a(2n) = A083420(n) - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), May 19 2005
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: 4kbasekseq[A*B] with A = + .25'i + .25'j + .25'k + .25i' + .25j' + .25k' + .25'ii' + .25'jj' + .25'kk' + .25'ij' + .25'ik' + .25'ji' + .25'jk' + .25'ki' + .25'kj' + .25e and B = + .5'i + .5i' + 'ii' + e - Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), May 19 2005
(PARI) a(n) = polresultant(x^n - 1, 2*x^2 - 1) (Wasserman)
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CROSSREFS
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Cf. A083420, A028400, A062510, A088037, A107663.
Cf. A060867.
Sequence in context: A113124 A030404 A066930 this_sequence A131623 A032011 A083203
Adjacent sequences: A085900 A085901 A085902 this_sequence A085904 A085905 A085906
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KEYWORD
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nonn
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AUTHOR
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Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 16 2003
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EXTENSIONS
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More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Feb 10 2005
Edited by njas at the suggestion of Andrew Plewe, Jun 15 2007
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