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A152602
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A symmetrical vector coefficient recursion sequence: a(n)=2*{0,a(n-2,0}+2*{-1/2,a(n-1)}+2*{a(n-1),-1/2}.
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0
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1, 1, 1, 1, 6, 1, 1, 16, 16, 1, 1, 36, 76, 36, 1, 1, 76, 256, 256, 76, 1, 1, 156, 736, 1176, 736, 156, 1, 1, 316, 1936, 4336, 4336, 1936, 316, 1, 1, 636, 4816, 14016, 19696, 14016, 4816, 636, 1, 1, 1276, 11536, 41536, 76096, 76096, 41536, 11536, 1276, 1, 1, 2556
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,5
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COMMENTS
| Row sums are;
{1, 2, 8, 34, 150, 666, 2962, 13178, 58634, 260890, 1160826,...}
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FORMULA
| a(n)=2*{0,a(n-2,0}+2*{-1/2,a(n-1)}+2*{a(n-1),-1/2}.
T(n,k) = 2T(n-2,k-1)+2T(n-1,k-1)+2T(n-1,k), 0<k<n, n>1. T(n,0) = 2T(n-1,0)-1, n>1. T(n,n) = 2T(n-1,n-1)-1, n>1. Row sum recurrence: s(n)=5*s(n-1)-2*s(n-2)-2*s(n-3), s=sum_(k=0..n) T(n,k). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 10 2008]
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EXAMPLE
| {1},
{1, 1},
{1, 6, 1},
{1, 16, 16, 1},
{1, 36, 76, 36, 1},
{1, 76, 256, 256, 76, 1},
{1, 156, 736, 1176, 736, 156, 1},
{1, 316, 1936, 4336, 4336, 1936, 316, 1},
{1, 636, 4816, 14016, 19696, 14016, 4816, 636, 1},
{1, 1276, 11536, 41536, 76096, 76096, 41536, 11536, 1276, 1},
{1, 2556, 26896, 115776, 263296, 343776, 263296, 115776, 26896, 2556, 1}
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MATHEMATICA
| Clear[a]; a[0] = {1}; a[1] = {1, 1};
a[n_] := a[n] = 2*Join[{0}, a[n - 2], {0}] + 2*Join[{-1/2}, a[n - 1]] + 2*Join[a[n - 1], {-1/2}]'
Table[a[n], {n, 0, 10}] Flatten[%]
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CROSSREFS
| Sequence in context: A109001 A203005 A176560 * A119726 A103999 A154985
Adjacent sequences: A152599 A152600 A152601 * A152603 A152604 A152605
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KEYWORD
| nonn,uned,tabl,obsc
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Dec 09 2008
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