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Search: id:A106632
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| A106632 |
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G.f. (1+27x^2)/[(1+3x)*(1-2x+9x^2) ]. |
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+0
1
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| -1, 1, -25, 49, -1, 529, -1849, 289, -9025, 58081, -38809, 108241, -1560001, 2283121, -525625, 35796289, -95863681, 2666689, -681575449, 3261894769, -1289169025, 9906021841, -94109673529, 99199171681, -84332740801, 2327696411041, -4753075824025, 46970592529, -48635546218561
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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S. Severini, A note on two integer sequences arising from the 3-dimensional hypercube, Technical Report, Department of Computer Science, University of Bristol, Bristol, UK (October 2003).
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FORMULA
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a(n) = (3^(n+1)/2)*(cos((n+1)*arccos(1/3)) + (-1)^(n+1) ).
Recurrence: a(n) = - a(n-1) - 3*a(n-2) - 27*a(n-3), a(0) = -1, a(1) = 1, a(2) = -25.
a(n) = 1/4( p^(n+1) + q^(n+1) ) + (-3)^(n+1)/2 with p = 1 + 2*sqrt(2)i and q = 1 - 2*sqrt(2)i ( i^2 = -1 ).
a(n) = ((-1)^(n+1))*(A087455(n+1))^2; 2*a(n) = A025172(n) + (-3)^(n+1).
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: 1tesseq[A*B] with A = + .5'i - .5'k + .5i' - .5k' - 3'jj' - .5'ij' - .5'ji' - .5'jk' - .5'kj' and B = + .5'i + .5'j + .5i' + .5j' + .5'kk' + .5'ij' + .5'ji' + .5e
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CROSSREFS
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Cf. A087455, A025172.
Sequence in context: A028505 A154082 A143278 this_sequence A090093 A004936 A062058
Adjacent sequences: A106629 A106630 A106631 this_sequence A106633 A106634 A106635
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KEYWORD
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sign
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), May 11 2005
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EXTENSIONS
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Edited by R. Stephan, Apr 09 2009
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