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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| In reference to program code, 2baseiseq[X](n) = ((-1)^n)*A001353(n) (a(n)^2 + 1 is a perfect square.) 1tesseq[X](n) = (-1^(n+1))*A097948(n)
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LINKS
| Robert Munafo, Sequences Related to Floretions
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FORMULA
| G.f.: (x^2+x+1)/((1-x)*(x+1)*(x^2+4*x+1)).
Floor(((2 + sqrt(3))^n + (2 - sqrt(3))^n)/4) produces this sequence with a different offset and without signs. - Jim Buddenhagen, May 20 2010
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
| 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[X] with X = .5'i + .5i' + 'ii' - .5'jj' + 1.5'kk' - 1
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CROSSREFS
| Cf. A007654, A001570, A076139. See also A117808, A122571 (same except for signs).
Sequence in context: A193164 A122424 A027326 * A048482 A094978 A178934
Adjacent sequences: A108943 A108944 A108945 * A108947 A108948 A108949
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KEYWORD
| easy,sign
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jul 21 2005
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EXTENSIONS
| Corrected floretion by Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Dec 11 2009
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