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A038223
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Bottom line of 3-wave sequence A038196, also bisection of A006356.
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2
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1, 6, 31, 157, 793, 4004, 20216, 102069, 515338, 2601899, 13136773, 66326481, 334876920, 1690765888, 8536537209, 43100270734, 217609704247, 1098693409021, 5547212203625, 28007415880892, 141407127676248
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Suggested by the Steinbach heptagon polynomial p^3 - p^2*(1 - p) - 2*p(1 - p)^2 + (1 - p)^3 = (1 - 5 p + 6 p^2 - p^3). - Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 20 2006
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REFERENCES
| Peter Steinbach, "Golden Fields: A Case for the Heptagon", Mathematics Magazine, Vol. 70, No. 1, Feb. 1997.
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LINKS
| F. v. Lamoen, Wave sequences
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FORMULA
| Let v(3)=(1, 1, 1), let M(3) be the 3 X 3 matrix m(i, j) =min(i, j), so M(3)=(1, 1, 1)/(1, 2, 2)/(1, 2, 3); then a(n)= Max ( v(3)*M(3)^n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 03 2002
G.f.: 1/(1-6x+5x^2-x^3). - Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 20 2006
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MATHEMATICA
| p[x_] := 1 - 5 x + 6 x^2 - x^3; q[x_] := ExpandAll[x^3*p[1/x]]; Table[ SeriesCoefficient[ Series[x/q[x], {x, 0, 30}], n], {n, 0, 30}] - Roger Bagula (rlbagulatftn(AT)yahoo.com), Sep 20 2006
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PROG
| (PARI) k=3; M(k)=matrix(k, k, i, j, min(i, j)); v(k)=vector(k, i, 1); a(n)=vecmax(v(k)*M(k)^n)
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CROSSREFS
| Sequence in context: A026771 A065096 A077352 * A022034 A047665 A003128
Adjacent sequences: A038220 A038221 A038222 * A038224 A038225 A038226
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KEYWORD
| nonn
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AUTHOR
| Floor van Lamoen (fvlamoen(AT)hotmail.com)
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EXTENSIONS
| More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 03 2002
Edited by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2008
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