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Search: id:A038342
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| A038342 |
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G.f.: -1/(- 1 + 3 x + 3 x^2 - 4 x^3 - x^4 + x^5) |
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+0
2
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| 1, 3, 12, 41, 146, 511, 1798, 6314, 22187, 77946, 273856, 962142, 3380337, 11876254, 41725295, 146595013, 515037713, 1809501081, 6357387289, 22335644540, 78472648463, 275700866485, 968630080476, 3403123989780
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Middle line of 5-wave sequence A038201.
Let M denotes the 5 X 5 matrix = row by row (1,1,1,1,1)(1,1,1,1,0)(1,1,1,0,0)(1,1,0,0,0)(1,0,0,0,0) and A(n) the vector (x(n),y(n),z(n),t(n),u(n))=M^n*A where A is the vector (1,1,1,1,1) then a(n)=z(n) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 02 2002
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REFERENCES
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Jay Kappraff, Beyond Measure, A Guided Tour Through Nature, Myth and Number, World Scientific, 2002.
P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
F. v. Lamoen, Wave sequences
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FORMULA
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a(n)=3a(n-1)+3a(n-2)-4a(n-3)-a(n-4)+a(n-5). Also a(n)=b(4n+2) with b(n) as in 5-wave sequence A038201.
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MATHEMATICA
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b = {-1, 3, 3, -4, -1, 1}; p[x_] := Sum[x^(n - 1)*b[[7 - n]], {n, 1, 6}] q[x_] := ExpandAll[x^5*p[1/x]] Table[ SeriesCoefficient[ Series[x/q[x], {x, 0, 30}], n], {n, 0, 30}] - Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 19 2006
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CROSSREFS
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Cf. A006358: same recurrence formula.
Cf. A066170.
Sequence in context: A038345 A127120 A017940 this_sequence A135264 A084529 A017941
Adjacent sequences: A038339 A038340 A038341 this_sequence A038343 A038344 A038345
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KEYWORD
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nonn
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com)
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 02 2002
Edited by N. J. A. Sloane (njas(AT)research.att.com) at the suggestion of Andrew Plewe, Jun 08 2007
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