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A165211
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Period 8: repeat [0,1,0,1,1,0,1,0].
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5
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0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 0
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OFFSET
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0,1
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COMMENTS
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Parity of A064706.
Parity of the generalized pentagonal numbers A001318. - Omar E. Pol, Feb 04 2012
More generally, parity of the generalized k-gonal numbers, for odd k >= 5. - Omar E. Pol, Feb 05 2012
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,-1,1).
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FORMULA
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a(n) = (1/56)*((n mod 8) + 8*((n+1) mod 8) - 6*((n+2) mod 8) + 8*((n+3) mod 8) + ((n+4) mod 8) - 6*((n+5) mod 8) + 8*((n+6) mod 8) - 6*((n+7) mod 8)), with n >= 0. - Paolo P. Lava, Sep 16 2009
a(n) = A002817(n) mod 2. - Wesley Ivan Hurt, Apr 23 2014
a(n) = 1/2 - (-1)^(n*(n+1)*(n^2 + n + 2)/8)/2. - Vaclav Kotesovec, Apr 28 2014
From Colin Barker, Dec 20 2017: (Start)
G.f.: x*(1 - x + x^2) / ((1 - x)*(1 + x^4)).
a(n) = a(n-1) - a(n-4) + a(n-5) for n>4.
(End)
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MATHEMATICA
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PadRight[{}, 112, {0, 1, 0, 1, 1, 0, 1, 0}] (* Harvey P. Dale, Jan 29 2012 *)
Table[Mod[n*(n+1)*(n^2+n+2)/8, 2], {n, 0, 100}] (* Vaclav Kotesovec, Apr 28 2014 after Wesley Ivan Hurt *)
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PROG
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(PARI) a(n)=bitxor(n, n\4)%2 \\ Charles R Greathouse IV, Jul 13 2016
(PARI) concat(0, Vec(x*(1 - x + x^2) / ((1 - x)*(1 + x^4)) + O(x^100))) \\ Colin Barker, Dec 20 2017
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CROSSREFS
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Cf. A001318, A002817, A064706.
Cf. A130198 (essentially the same).
Sequence in context: A285249 A269027 A089809 * A341389 A188027 A359333
Adjacent sequences: A165208 A165209 A165210 * A165212 A165213 A165214
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KEYWORD
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nonn,easy
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AUTHOR
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Philippe Deléham, Sep 07 2009
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STATUS
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approved
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