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Search: id:A108946
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| 1, -3, 13, -48, 181, -675, 2521, -9408, 35113, -131043, 489061, -1825200, 6811741, -25421763, 94875313, -354079488, 1321442641, -4931691075, 18405321661, -68689595568, 256353060613, -956722646883, 3570537526921, -13325427460800, 49731172316281
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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In reference to program code, 2baseiseq[A*B](n) = ((-1)^n)*A001353(n) (a(n)^2 + 1 is a perfect square.) 1tesseq[A*B](n) = (-1^(n+1))*A097948(n)
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FORMULA
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G.f. (x^2+x+1)/((1-x)*(x+1)*(x^2+4*x+1)) Define c(n) = a(n) - 4*a(n+1) - a(n+2) and d(n) = -a(n) - 4*a(n+1) - a(n+2); Conjectures: I: c(2n) = 24*A076139(n); (Triangular numbers that are one-third of another triangular number) II: c(2n+1) = -A011943(n+1); (Numbers n such that any group of n consecutive integers has integral standard deviation) III: d(2n) = -2; IV: d(2n+1) = -1
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MAPLE
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seriestolist(series((x^2+x+1)/((1-x)*(x+1)*(x^2+4*x+1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1ibaseiseq[A*B] with A = + .5'i - .5'k + .5i' - .5k' - 'jj' - .5'ij' - .5'ji' - .5'jk' - .5'kj' and B = + .5'i + .5i' + .5'jj' + .5'kk'
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CROSSREFS
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Cf. A007654, A001570, A076139.
Sequence in context: A084519 A122424 A027326 this_sequence A048482 A094978 A045908
Adjacent sequences: A108943 A108944 A108945 this_sequence A108947 A108948 A108949
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KEYWORD
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easy,sign
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jul 21 2005
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