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Search: id:A103750
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| A103750 |
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Kenyon tile Fibonacci-like sequence fourth power. |
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+0
1
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| 1, 1, 1, 2, 3, 1, 8, 13, 3, 26, 55, 35, 72, 217, 215, 146, 795, 1079, 8, 2677, 4827, 2134, 8047, 19835, 16056, 19873, 75599, 87838, 27507, 266543, 414712, 93155, 854643, 1777222, 1108889, 2377619, 7040952, 6881111, 4915079, 25878094, 34725237
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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x^n-p*x^(n-1)+q*x+r=0 n=4,p=2,q=-1,r=-1
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LINKS
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Richard Kenyon, The Construction of Self-Similar Tilings
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FORMULA
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b[n]=b[n-1]-b[n-3]+2*b[n-4] a(n)=Abs[b[n]]
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MATHEMATICA
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(* derivation from Kenyon's equations*) r = -1; p = 2; q = -1; M = {{0, 1, 0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {-r, 0, q, p}} Det[M - x*IdentityMatrix[4]] NSolve[Det[M - x*IdentityMatrix[4]] == 0, x] M.{a[n - 1], a[n - 2], a[n - 3], a[n - 4]} (* sequence*) a[0] = 1; a[1] = 1; a[2] = 1; a[n_Integer?Positive] := a[n] = 2* a[ -4 + n] - a[ -3 + n] + a[ -1 + n]; aa = Table[a[n], {n, 0, 200}] b=Abs[aa]
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CROSSREFS
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Cf. A073058, A099206.
Sequence in context: A110292 A138672 A103749 this_sequence A098435 A096294 A135950
Adjacent sequences: A103747 A103748 A103749 this_sequence A103751 A103752 A103753
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 28 2005
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