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A346434
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Triangle read by rows of numbers with n 1's and n 0's in their representation in base of Fibonacci numbers (A210619), written as those 1's and 0's.
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2
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10, 1001, 1010, 100101, 101001, 101010, 10010101, 10100101, 10101001, 10101010, 1001010101, 1010010101, 1010100101, 1010101001, 1010101010, 100101010101, 101001010101, 101010010101, 101010100101, 101010101001, 101010101010
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refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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The digits of T(n,k) are k pairs 10 followed by n-k pairs 01.
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LINKS
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FORMULA
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T(n,k) = (10*100^n - 9*100^(n-k) - 1)/99, for n>=1 and 1 <= k <= n.
G.f.: x*y*(10 - 9*x - 100*x^2*y) / ((1-x) * (1-100*x) * (1-x*y) * (1-100*x*y) ).
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EXAMPLE
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Triangle begins:
k=1 k=2 k=3 k=4
n=1: 10
n=2: 1001, 1010,
n=3: 100101, 101001, 101010,
n=4: 10010101, 10100101, 10101001, 10101010
...
For n=5,k=3, the 10 and 01 digit pairs are
vvvvvv k = 3 pairs 10
T(5,3) = 1010100101
^^^^ n-k = 2 pairs 01
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PROG
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(PARI) T(n, k) = (10*100^n - 9*100^(n-k)) \ 99;
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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