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Search: id:A126770
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| 1, 1, 1, 1, 2, 1, 1, 4, 4, 1, 1, 7, 16, 7, 1, 1, 12, 53, 53, 12, 1, 1, 20, 166, 318, 166, 20, 1, 1, 33, 492, 1784, 1784, 492, 33, 1, 1, 54, 1413, 9288, 17840, 9288, 1413, 54, 1, 1, 88, 3960, 46233, 163504, 163504, 46233, 3960, 88, 1, 1, 143, 10912, 221859, 1418549
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row sums are {1, 2, 4, 10, 32, 132, 692, 4620, 39352, 427572, ...}. - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 09 2008
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FORMULA
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T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,k)=F(n-k+1)*T(n-1,k-1)+F(k+1)*T(n-1,k) wher F(n)=Fibonacci(n)=A000045(n).
T(n,k)=Fibonacci[(n - k + 1)]*A(n - 1, k - 1) + Fibonacci[k ]*A(n - 1, k). - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 09 2008
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 2, 1;
1, 4, 4, 1;
1, 7, 16, 7, 1;
1, 12, 53, 53, 12, 1;
1, 20, 166, 318, 166, 20, 1;
1, 33, 492, 1784, 1784, 492, 33, 1;
1, 54, 1413, 9288, 17840, 9288, 1413, 54, 1;
1, 88, 3960, 46233, 163504, 163504, 46233, 3960, 88, 1;
1, 143, 10912, 221859, 1418549, 2616064, 1418549, 221859, 10912, 143, 1;
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MATHEMATICA
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T[n_, 1] := 1; T[n_, n_] := 1; T[n_, k_] := Fibonacci[(n - k + 1)]*T[ n - 1, k - 1] + Fibonacci[k ]*T[n - 1, k]; Table[Table[T[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%] - Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Sep 09 2008
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CROSSREFS
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Column sequences :A000012, A000071, A056589-91; A056592(Row sums).
Sequence in context: A104382 A086629 A156184 this_sequence A056588 A156006 A137854
Adjacent sequences: A126767 A126768 A126769 this_sequence A126771 A126772 A126773
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KEYWORD
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nonn,tabl
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 17 2007
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