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A141604
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Combination-like triangle of coefficients made using Somos4 ;A006720; t(n,m)=A0006720(n)/(A0006720(n-m)*A0006720(m)).
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0
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1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 2, 3, 3, 2, 1, 1, 2, 4, 7, 4, 2, 1, 1, 3, 8, 12, 12, 8, 3, 1, 1, 3, 8, 20, 15, 20, 8, 3, 1, 1, 5, 14, 45, 52, 52, 45, 14, 5, 1, 1, 5, 26, 66, 109, 170, 109, 66, 26, 5, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,12
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COMMENTS
| Row sums are:
{1, 2, 3, 4, 8, 12, 21, 48, 79, 234, 584}.
A lot about the Somos(n) sequences is explained if they are behaving like modified permutations.
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FORMULA
| t(n,m)=A0006720(n)/(A0006720(n-m)*A0006720(m)).
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EXAMPLE
| {1},
{1, 1},
{1, 1, 1},
{1, 1, 1, 1},
{1, 2, 2, 2, 1},
{1, 2, 3, 3, 2, 1},
{1, 2, 4, 7, 4, 2, 1},
{1, 3, 8, 12, 12, 8, 3, 1},
{1, 3, 8, 20, 15, 20, 8, 3, 1},
{1, 5, 14, 45, 52, 52, 45, 14, 5, 1},
{1, 5, 26, 66, 109, 170, 109, 66, 26, 5, 1}
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MATHEMATICA
| Clear[a, t] (*A006720*) (*Robert G.Wilson v (rgwv(AT)rgwv.com), Jul 04 2007*) a[0] = a[1] = a[2] = a[3] = 1; a[n_] := a[n] = (a[n - 1] a[n - 3] + a[n - 2]^2)/a[n - 4]; Array[a, 23]; t[n_, m_] := a[n]/(a[n - m]*a[m]) Table[Table[Round[t[n, m]], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
| Cf. A006720.
Sequence in context: A190321 A134143 A085684 * A143996 A171412 A071338
Adjacent sequences: A141601 A141602 A141603 * A141605 A141606 A141607
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KEYWORD
| nonn,uned,tabl
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Aug 21 2008
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