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Search: id:A121961
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| A121961 |
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G.f.: 1/(1-12*x^2-8*x^3+36*x^4+32*x^5-32*x^6-32*x^7). |
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+0
1
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| 1, 0, 12, 8, 108, 160, 960, 2144, 9040, 24832, 89664, 270976, 916416, 2885120, 9500160, 30412288, 99084544, 319299584, 1035979776, 3347073024, 10842246144, 35064422400, 113514577920, 367253348352, 1188632055808, 3846143410176, 12447083347968, 40278203727872
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Bsed on characteristic polynomial of a square-within-a-square bonding graph.
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FORMULA
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Factors of denominator of g.f.: -(2*x+1)*(4*x^2+2*x-1)*(-1+2*x^2)^2.
Let M be the 8 X 8 matrix {{0, 1, 0, 1, 1, 0, 0, 1}, {1, 0, 1, 0, 1, 1, 0, 0}, {0, 1, 0, 1, 0, 1, 1, 0}, {1, 0, 1, 0, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0}, {1, 0, 0, 1, 0, 0, 0, 0}}; then the g.f. is essentially the reciprocal of Det[M - x*IdentityMatrix[8]].
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MATHEMATICA
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M = {{0, 1, 0, 1, 1, 0, 0, 1}, {1, 0, 1, 0, 1, 1, 0, 0}, {0, 1, 0, 1, 0, 1, 1, 0}, {1, 0, 1, 0, 0, 0, 1, 1}, {1, 1, 0, 0, 0, 0, 0, 0}, {0, 1, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 1, 0, 0, 0, 0}, {1, 0, 0, 1, 0, 0, 0, 0}} f[x_] = Det[M - x*IdentityMatrix[8]] a=Table[ SeriesCoefficient[ Series[x/(x^10*f[1/x]), {x, 0, 30}], n], {n, 0, 30}]
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CROSSREFS
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Sequence in context: A118656 A094332 A040134 this_sequence A038334 A101501 A018870
Adjacent sequences: A121958 A121959 A121960 this_sequence A121962 A121963 A121964
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 02 2006
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EXTENSIONS
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Edited by njas, Feb 01 2007
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