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Search: id:A083856
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| A083856 |
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Square array of generalized Fibonacci numbers, read by antidiagonals. |
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+0
7
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| 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 2, 1, 0, 1, 1, 3, 3, 1, 0, 1, 1, 4, 5, 5, 1, 0, 1, 1, 5, 7, 11, 8, 1, 0, 1, 1, 6, 9, 19, 21, 13, 1, 0, 1, 1, 7, 11, 29, 40, 43, 21, 1, 0, 1, 1, 8, 13, 41, 65, 97, 85, 34, 1, 0, 1, 1, 9, 15, 55, 96, 181, 217, 171, 55, 1
(list; table; graph; listen)
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OFFSET
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0,14
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COMMENT
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Array gives solutions to the recurrences a(n)=a(n-1)+ka(n-2),a(0)=0,a(1)=1,k>=0. Rows include A000045, A001045, A006130, A006131, A015440, A015441, A015441, A015442, A015443, A015445.
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FORMULA
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T(n, k)=(1+(sqrt(4k+1))/2)^n/sqrt(4k+1)-((1-sqrt(4k+1))/2)^n/sqrt(4k+1)
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EXAMPLE
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Rows begin
0 1 1 1 1 1 ...
0 1 1 2 3 5 ...
0 1 1 3 5 11 ...
0 1 1 4 7 19 ...
0 1 1 5 9 29 ...
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CROSSREFS
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Cf. A083857.
Sequence in context: A131255 A133607 A103631 this_sequence A081718 A129634 A066438
Adjacent sequences: A083853 A083854 A083855 this_sequence A083857 A083858 A083859
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 06 2003
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