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A205651
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Period 6: repeat (1, 6, 5, 4, 9, 0).
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0
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1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6, 5, 4, 9, 0, 1, 6
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OFFSET
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1,2
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COMMENTS
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The members of this sequence are also the units' digits of the indices of those non-zero square numbers that are also triangular.
The coefficients of x^n in the numerator of the generating function form the periodic cycle of the sequence.
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LINKS
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Table of n, a(n) for n=1..86.
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
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FORMULA
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G.f. x*(1+6*x+5*x^2+4*x^3+9*x^4) / ((1-x)*(1+x)*(1-x+x^2)*(1+x+x^2)).
a(n) = a(n-6).
a(n) = 25-a(n-1)-a(n-2)-a(n-3)-a(n-4)-a(n-5).
For n>0, a(n) = A010879(A001109(n)) = A010879(sqrt(A001110(n))) = mod(A001109(n),10).
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EXAMPLE
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The fourth non-zero square number that is also a triangular number is 204^2. As 204 has units' digit 4, then a(4)=4.
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MATHEMATICA
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LinearRecurrence[{0, 0, 0, 0, 0, 1}, {1, 6, 5, 4, 9, 0}, 86]
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PROG
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(PARI) a(n)=[0, 1, 6, 5, 4, 9][n%6+1] \\ Charles R Greathouse IV, Jan 31 2012
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CROSSREFS
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Cf. A010879, A001109, A001110.
Sequence in context: A200096 A220086 A094773 * A168239 A019131 A019132
Adjacent sequences: A205648 A205649 A205650 * A205652 A205653 A205654
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KEYWORD
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nonn,easy,changed
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AUTHOR
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Ant King, Jan 31 2012
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STATUS
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approved
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