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A017125
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Table read by antidiagonals of Fibonacci-type sequences.
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1
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0, 1, 1, 1, 1, 2, 2, 2, 1, 3, 3, 3, 3, 1, 4, 5, 5, 4, 4, 1, 5, 8, 8, 7, 5, 5, 1, 6, 13, 13, 11, 9, 6, 6, 1, 7, 21, 21, 18, 14, 11, 7, 7, 1, 8, 34, 34, 29, 23, 17, 13, 8, 8, 1, 9, 55, 55, 47, 37, 28, 20, 15, 9, 9, 1, 10, 89, 89, 76, 60, 45, 33, 23, 17, 10, 10, 1, 11, 144, 144, 123, 97, 73
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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LINKS
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FORMULA
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T(n, k) = T(n, k-1)+T(n, k-2) [with T(n, 0) = n and T(n, 1) = 1] = 2*T(n-1, k)-T(n-2, k) = Fib(k)+n*Fib(k-1) = (s^k*(1+2n/s)-t^k*(1+2n/t))/(2^k*sqrt(5)) where s = (1+sqrt(5))/2 and t = (1-sqrt(5))/2 = 1-s.
G.f. for n-th row: (n+x-nx)/(1-x-x^2).
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CROSSREFS
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Rows are (essentially) A000045, A000045, A000032, A000285, A022095, A022096, A022097, etc. Columns are (essentially) A001477, A000012, A000027, A005408, A016789, A016885, etc. One of the diagonals is A007502.
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KEYWORD
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AUTHOR
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STATUS
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approved
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