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A088917
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Central Delannoy numbers (mod 3).
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1
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1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Also Apery numbers (mod 3). More generally also sum(k=0,n,binomial(n,k)^x*binomial(n+k,k)^y) (mod 3) for any x>=1 in N and any odd y>=1.
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LINKS
| Eric Weisstein's World of Mathematics, Cantor Fractal
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FORMULA
| a(A005823(n))=1; a(A081606(n))=0
a(n)=A001850(n)-3*floor(A001850(n)/3)
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MATHEMATICA
| Nest[ Flatten[# /. {0 -> {0, 0, 0}, 1 -> {1, 0, 1}}] &, {1}, 5] (* Or *)
f[n_] := Mod[LegendreP[n, 3], 3]; Array[f, 111, 0] (* Or *)
f[n_] := If[ FreeQ[ IntegerDigits[n, 3], 1], 1, 0]; Array[f, 111, 0] (* Robert G. Wilson v, Jun 16 2011 *)
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PROG
| (PARI) a(n)=sum(k=0, n, binomial(n, k)*binomial(n+k, k))%3
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CROSSREFS
| Cf. A005823, A005258, A081606, A001850.
Sequence in context: A102242 A005369 A108340 * A014933 A011643 A015941
Adjacent sequences: A088914 A088915 A088916 * A088918 A088919 A088920
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 30 2003
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