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Search: id:A129858
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| A129858 |
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A triangle of coefficients based on A000217: a(n)=Binomial[n+2,2]; t(n,m)=a(n - m + 1)*a(m + 1) - a((n - m + 1)*(m + 1)). |
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+0
1
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| 6, 12, 12, 20, 21, 20, 30, 32, 32, 30, 42, 45, 45, 45, 42, 56, 60, 59, 59, 60, 56, 72, 77, 74, 72, 74, 77, 72, 90, 96, 90, 84, 84, 90, 96, 90, 110, 117, 107, 95, 90, 95, 107, 117, 110, 132, 140, 125, 105, 92, 92, 105, 125, 140, 132, 156, 165, 144, 114, 90, 81, 90, 114, 144
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are:
{6, 24, 61, 124, 219, 350, 518, 720, 948, 1188, 1419}.
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REFERENCES
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G. E. Andrews, Number Theory, 1971, Dover Publications New York, p 44,p 85.
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FORMULA
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a(n)=Binomial[n+2,2]; t(n,m)=a(n - m + 1)*a(m + 1) - a((n - m + 1)*(m + 1)).
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EXAMPLE
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{6},
{12, 12},
{20, 21, 20},
{30, 32, 32, 30},
{42, 45, 45, 45, 42},
{56, 60, 59, 59, 60, 56},
{72, 77, 74, 72, 74, 77, 72},
{90, 96, 90, 84, 84, 90, 96, 90},
{110, 117, 107, 95, 90, 95, 107, 117, 110},
{132, 140, 125, 105, 92, 92, 105, 125, 140, 132},
{156, 165, 144, 114, 90, 81, 90, 114, 144, 165, 156}
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MATHEMATICA
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Clear[a, n, m, t] (*A000217*) a[0] = 1; a[1] = 3; a[n_] := a[n] = Binomial[n + 2, 2]; Table[a[n], {n, 0, 30}]; t[n_, m_] = FullSimplify[a[n - m + 1]*a[m + 1] - a[(n - m + 1)*(m + 1)]]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Cf. A000217.
Sequence in context: A040030 A135462 A156386 this_sequence A061928 A070149 A055595
Adjacent sequences: A129855 A129856 A129857 this_sequence A129859 A129860 A129861
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KEYWORD
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nonn,tabl
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Aug 25 2008
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