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A101101
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a(1)=1, a(2)=5, and a(n)=6 for n>=3.
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3
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1, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6
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OFFSET
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1,2
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COMMENTS
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Previous name was: The first summation of row 3 of Euler's triangle - a row that will recursively accumulate to the power of 3.
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LINKS
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FORMULA
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MATHEMATICA
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MagicNKZ=Sum[(-1)^j*Binomial[n+1-z, j]*(k-j+1)^n, {j, 0, k+1}]; Table[MagicNKZ, {n, 3, 3}, {z, 1, 1}, {k, 0, 34}] (* OR *)
SeriesAtLevelR = Sum[Eulerian[n, i - 1]*Binomial[n + x - i + r, n + r], {i, 1, n}]; Table[SeriesAtLevelR, {n, 3, 3}, {r, -3, -3}, {x, 4, 35}]
Join[{1, 5}, LinearRecurrence[{1}, {6}, 78]] (* Ray Chandler, Sep 23 2015 *)
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CROSSREFS
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Within the "cube" of related sequences with construction based upon MaginNKZ formula, with n downward, k rightward and z backward:
Within the "cube" of related sequences with construction based upon SeriesAtLevelR formula, with n downward, x rightward and r backward:
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KEYWORD
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easy,nonn,uned
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AUTHOR
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Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
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EXTENSIONS
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I wish the sequence was as interesting as the list of references! - N. J. A. Sloane
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STATUS
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approved
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