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Search: id:A129705
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| A129705 |
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Triangular array read by rows, from the projective variety of dimension of Fibonacci sequence as sum of Fibonacci to n minus m*(m+1)/2. |
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+0
1
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| 0, 1, 0, 2, 1, -1, 4, 3, 1, -2, 7, 6, 4, 1, -3, 12, 11, 9, 6, 2, -3, 20, 19, 17, 14, 10, 5, -1, 33, 32, 30, 27, 23, 18, 12, 5, 54, 53, 51, 48, 44, 39, 33, 26, 18, 88, 87, 85, 82, 78, 73, 67, 60, 52, 43, 143, 142, 140, 137, 133, 128, 122, 115, 107, 98, 88
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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Absolute value row sum is: Table[Apply[Plus, Abs[Table[t[n, m], {m, 0, n}]]], {n, 0, 10}]; {0, 1, 4, 10, 21, 43, 86, 180, 366, 715, 1353} Which appears to be new as well.
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LINKS
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Eric Weisstein's World of Mathematics, Schubert Variety
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FORMULA
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t(n,m)=Sum[A000045[i],{i,0,n}]-Sum[i,{i,0,m}]
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EXAMPLE
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{0},
{1, 0},
{2, 1, -1},
{4, 3, 1, -2},
{7, 6, 4, 1, -3},
{12, 11, 9, 6, 2, -3},
{20, 19, 17, 14, 10, 5, -1},
{33, 32, 30, 27, 23, 18, 12, 5}
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MATHEMATICA
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fib[n_Integer?Positive] := fib[n] = fib[n - 1] + fib[n - 2]; fib[0] = 0; fib[1] = fib[2] = 1; t[n_, m_] = Sum[fib[i], {i, 0, n}] - Sum[i, {i, 0, m}]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]
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CROSSREFS
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Cf. A000045.
Sequence in context: A070895 A127054 A125790 this_sequence A074744 A010360 A112744
Adjacent sequences: A129702 A129703 A129704 this_sequence A129706 A129707 A129708
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 08 2007
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