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Search: id:A033190
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| A033190 |
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Sum(binomial(n,k)*binomial(fibonacci(k)+1,2),k=0..n). |
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+0
1
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| 0, 1, 3, 9, 28, 90, 297, 1001, 3431, 11917, 41820, 147918, 526309, 1881009, 6744843, 24244145, 87300092, 314765506, 1135980801, 4102551897, 14823628015, 53581222773, 193724727804, 700551945014
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OFFSET
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0,3
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COMMENT
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Number of (s(0), s(1), ..., s(2n)) such that 0 < s(i) < 10 and |s(i) - s(i-1)| = 1 for i = 1,2,....,2n, s(0) = 1, s(2n) = 3. - Herbert Kociemba (kociemba(AT)t-online.de), Jun 14 2004
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FORMULA
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G.f.: (-x^4+6x^3-5x^2+x)/[(1-3x+x^2)(1-5x+5x^2)].
a(n)=(1/5)*Sum(r, 1, 9, Sin(r*Pi/10)Sin(3*r*Pi/10)(2Cos(r*Pi/10))^(2n)), n>=1 a(n)=8a(n-1)-21a(n-2)+20a(n-3)-5a(n-4), n>=5 - Herbert Kociemba (kociemba(AT)t-online.de), Jun 14 2004
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CROSSREFS
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Sequence in context: A094164 A094803 A094826 this_sequence A071724 A000245 A047047
Adjacent sequences: A033187 A033188 A033189 this_sequence A033191 A033192 A033193
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KEYWORD
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nonn
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AUTHOR
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njas
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