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A144656
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a(n) = (n mod 2) if n <= 3, otherwise a(n) = (n^2-5n+7)*(n-2)*a(n-1)/(n-3) + (n^2-5n+7)*a(n-2) - (n-2)*a(n-3)/(n-3).
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1
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0, 1, 0, 1, 4, 49, 900, 24649, 944784, 48455521, 3210355600, 267186643801, 27307626948900, 3363915436531441, 491705171699154084, 84158959760104032049, 16675767262618669710400, 3787671541267275818341249, 977702867682508392324162624, 284628954669920840314598014801
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OFFSET
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0,5
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COMMENTS
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Terms are squares; square roots give A001053.
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REFERENCES
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M. E. Larsen, Summa Summarum, A. K. Peters, Wellesley, MA, 2007; see p. 35.
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LINKS
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MAPLE
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a:=proc(n) option remember; local m;
if n=0 then RETURN(0); fi;
if n=1 then RETURN(1); fi;
if n=2 then RETURN(0); fi;
if n=3 then RETURN(1); fi;
m:=n-3;
RETURN((m^2+m+1)*(m+1)*a(n-1)/m+(m^2+m+1)*a(n-2)-(m+1)*a(n-3)/m);
end;
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PROG
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(PARI) a=vector(10^3); for(n=1, 3, a[n]=n%2); for(n=4, #a, a[n] = (n^2-5*n+7)*(n-2)*a[n-1]/(n-3) + (n^2-5*n+7)*a[n-2] - (n-2)*a[n-3]/(n-3)); concat(0, a) \\ Altug Alkan, Apr 04 2018
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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