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A131923
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Triangle read by rows: T(n,k) = binomial(n,k) + n.
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2
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1, 2, 2, 3, 4, 3, 4, 6, 6, 4, 5, 8, 10, 8, 5, 6, 10, 15, 15, 10, 6, 7, 12, 21, 26, 21, 12, 7, 8, 14, 28, 42, 42, 28, 14, 8, 9, 16, 36, 64, 78, 64, 36, 16, 9, 10, 18, 45, 93, 135, 135, 93, 45, 18, 10, 11, 20, 55, 130, 220, 262, 220, 130, 55, 20, 11, 12, 22, 66
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table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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Row sums = A131924: (1, 4, 10, 20, 36, 62, 106, 184, ...).
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LINKS
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FORMULA
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EXAMPLE
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First few rows of the triangle are:
1;
2, 2;
3, 4, 3;
4, 6, 6, 4;
5, 8, 10, 8, 5;
6, 10, 15, 15, 10, 6;
7, 12, 21, 26, 21, 12, 7;
8, 14, 28, 42, 42, 28, 14, 8;
9, 16, 36, 64, 78, 64, 36, 16, 9;
10, 18, 45, 93, 135, 135, 93, 45, 18, 10;
...
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MATHEMATICA
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T[n_, m_] = Binomial[n, m] + n; Table[Table[T[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%] (* Roger L. Bagula, Jul 30 2008 *)
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PROG
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(GAP) a:=Flat(List([0..10], n->List([0..n], k->Binomial(n, k)+n))); # Muniru A Asiru, Jul 16 2018
(Magma) /* As triangle */ [[Binomial(n, k) + n: k in [0..n]]: n in [0.. 15]]; // Vincenzo Librandi, Jul 17 2018
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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