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Search: id:A122504
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| A122504 |
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Bi_Steinbach heptagon recursion: a(n) = -a(n - 6) + 3 a(n - 5) + a(n - 4) - 7 a(n - 3) + a(n - 2) + 3 a(n - 1); characteristic polynomial: (x^3 - 2*x^2 - x + 1)*(x^3 - x^2 - 2*x + 1). |
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+0
1
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| 1, 1, 1, 1, 1, 1, 0, -3, -13, -39, -107, -273, -675, -1624, -3847, -8995, -20851, -47995, -109915, -250695, -570024, -1292915, -2926953, -6616051, -14936895, -33690357, -75931283, -171029936, -385046687, -866536007, -1949510615, -4384874471, -9860587191, -22170707871, -49842661456
(list; graph; listen)
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OFFSET
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1,8
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COMMENT
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Roots: aaa = Table[x /. NSolve[Det[M - x*IdentityMatrix[6]] == 0, x][[n]], {n, 1, 6}] {-1.24698, -0.801938, 0.445042, 0.554958, 1.80194, 2.24698} Sum of roots is an Integer 3: Apply[Plus, aaa]=3
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FORMULA
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O.g.f.: x(1-x-3x^2)(1-x-x^2)/((1-2x-x^2+x^3)(1-x-2x^2+x^3)). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 22 2008]
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MATHEMATICA
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a[0] = 1; a[1] = 1; a[2] = 1; a[3] = 1; a[4] = 1; a[5] = 1; a[n_] := a[n] = -a[n - 6] + 3 a[n - 5] + a[n - 4] - 7 a[n - 3] + a[n - 2] + 3 a[n - 1] Table[a[n], {n, 0, 30}] (* vector Matrix Markov*) M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {-1, 3, 1, -7, 1, 3}} v[1] = {1, 1, 1, 1, 1, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}]
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CROSSREFS
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Cf. A006054, A006053.
Sequence in context: A072790 A166911 A103657 this_sequence A103277 A147042 A018492
Adjacent sequences: A122501 A122502 A122503 this_sequence A122505 A122506 A122507
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KEYWORD
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sign
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 15 2006
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