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A142595
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Triangle read by rows: t(n,k)= 2*t(n - 1, k - 1) + 2* t(n - 1, k).
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0
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1, 1, 1, 1, 4, 1, 1, 10, 10, 1, 1, 22, 40, 22, 1, 1, 46, 124, 124, 46, 1, 1, 94, 340, 496, 340, 94, 1, 1, 190, 868, 1672, 1672, 868, 190, 1, 1, 382, 2116, 5080, 6688, 5080, 2116, 382, 1, 1, 766, 4996, 14392, 23536, 23536, 14392, 4996, 766, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| Symmetrical recursion of the Pascal triangle type.
Row sums are A047849.
This triangle sequence is dominated by the Eulerian numbers A008292.
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FORMULA
| a(n)=2*Join[a(n - 1), {-1/2}] + 2*Join[{-1/2}, a(n - 1)]. [From Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008]
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EXAMPLE
| {1},
{1, 1},
{1, 4, 1},
{1, 10, 10, 1},
{1, 22, 40, 22, 1},
{1, 46, 124, 124, 46, 1},
{1, 94, 340, 496, 340, 94, 1},
{1, 190, 868, 1672, 1672, 868, 190, 1},
{1, 382, 2116, 5080, 6688, 5080, 2116, 382, 1},
{1, 766, 4996, 14392, 23536, 23536, 14392, 4996, 766, 1}
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MATHEMATICA
| A[n_, 1] := 1 A[n_, n_] := 1 A[n_, k_] := A[n - 1, k - 1] + 2* A[n - 1, k] + A[n - 1, k - 1]; a = Table[A[n, k], {n, 10}, {k, n}]; Flatten[a]
Contribution from Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008: (Start)
Clear[a];
a[0] = {1}; a[1] = {1, 1};
a[n_] := a[n] = 2*Join[a[n - 1], {-1/2}] + 2*Join[{-1/2}, a[n - 1]];
Table[a[n], {n, 0, 10}];
Flatten[%] (End)
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CROSSREFS
| Cf. A008292, A119258.
Sequence in context: A082680 A056939 A202924 * A174669 A140711 A164366
Adjacent sequences: A142592 A142593 A142594 * A142596 A142597 A142598
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KEYWORD
| nonn,easy,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 22 2008
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 11 2008
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