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A156070
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Triangle read by rows based on the Fibonacci sequence A000045: t(n,m) = 1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m].
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1
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1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 3, 2, 1, 1, 3, 5, 5, 5, 3, 1, 1, 5, 8, 9, 9, 8, 5, 1, 1, 8, 13, 15, 16, 15, 13, 8, 1, 1, 13, 21, 25, 27, 27, 25, 21, 13, 1, 1, 21, 34, 41, 45, 46, 45, 41, 34, 21, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,13
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COMMENTS
| Row sums are {1, 2, 2, 4, 6, 12, 23, 46, 90, 174, 330,...} (see A188538).
More generally, we can define for a sequence with a(n)=0 : add one;
t(n,m)=1+a(n)-a(m)-a(n-m)
or a(0)=1: add two:
t(n,m)=2+a(n)-a(m)-a(n-m).
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FORMULA
| t(n,m)=1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m].
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EXAMPLE
| {1},
{1, 1},
{1, 0, 1},
{1, 1, 1, 1},
{1, 1, 2, 1, 1},
{1, 2, 3, 3, 2, 1},
{1, 3, 5, 5, 5, 3, 1},
{1, 5, 8, 9, 9, 8, 5, 1},
{1, 8, 13, 15, 16, 15, 13, 8, 1},
{1, 13, 21, 25, 27, 27, 25, 21, 13, 1},
{1, 21, 34, 41, 45, 46, 45, 41, 34, 21, 1}
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MATHEMATICA
| t[n_, m_] = 1 + Fibonacci[n] - Fibonacci[m] - Fibonacci[n - m];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]
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CROSSREFS
| Cf. A000045, A188538.
Sequence in context: A029344 A125769 A003023 * A114731 A035389 A129176
Adjacent sequences: A156067 A156068 A156069 * A156071 A156072 A156073
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KEYWORD
| nonn,tabl
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Feb 03 2009
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EXTENSIONS
| Edited by N. J. A. Sloane, Apr 03 2011
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