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Search: id:A144463
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| A144463 |
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A symmetrical triangle sequence: t(n,m)=Binomial[n, m]*2^If[m <= Floor[n/2], m, n - m]. |
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+0
1
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| 1, 1, 1, 1, 4, 1, 1, 6, 6, 1, 1, 8, 24, 8, 1, 1, 10, 40, 40, 10, 1, 1, 12, 60, 160, 60, 12, 1, 1, 14, 84, 280, 280, 84, 14, 1, 1, 16, 112, 448, 1120, 448, 112, 16, 1, 1, 18, 144, 672, 2016, 2016, 672, 144, 18, 1, 1, 20, 180, 960, 3360, 8064, 3360, 960, 180, 20, 1
(list; graph; listen)
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OFFSET
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1,5
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COMMENT
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Row sums are:
{1, 2, 6, 14, 42, 102, 306, 758, 2274, 5702, 17106}.
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FORMULA
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t(n,m)=Binomial[n, m]*2^If[m <= Floor[n/2], m, n - m].
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EXAMPLE
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{1},
{1, 1},
{1, 4, 1},
{1, 6, 6, 1},
{1, 8, 24, 8, 1},
{1, 10, 40, 40, 10, 1},
{1, 12, 60, 160, 60, 12, 1},
{1, 14, 84, 280, 280, 84, 14, 1},
{1, 16, 112, 448, 1120, 448, 112, 16, 1},
{1, 18, 144, 672, 2016, 2016, 672, 144, 18, 1},
{1, 20, 180, 960, 3360, 8064, 3360, 960, 180, 20, 1}
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MATHEMATICA
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Clear[f, t]; f[n_, m_] = If[m <= Floor[n/2], m, n - m]; t[n_, m_] = Binomial[n, m]*2^f[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
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CROSSREFS
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Sequence in context: A143188 A102413 A144480 this_sequence A131399 A069322 A075112
Adjacent sequences: A144460 A144461 A144462 this_sequence A144464 A144465 A144466
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Oct 09 2008
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