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A346006
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Successive numbers arising from the Moessner construction of the sequence of fourth powers on page 64 of Conway-Guy's "Book of Numbers".
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4
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0, 1, 4, 6, 4, 16, 32, 24, 8, 81, 108, 54, 12, 256, 256, 96, 16, 625, 500, 150, 20, 1296, 864, 216, 24, 2401, 1372, 294, 28, 4096, 2048, 384, 32, 6561, 2916, 486, 36, 10000, 4000, 600, 40, 14641, 5324, 726, 44, 20736, 6912, 864, 48, 28561, 8788, 1014, 52, 38416, 10976, 1176, 56, 50625, 13500, 1350, 60
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listen;
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OFFSET
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0,3
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COMMENTS
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a(4*k+1) = (k+1)^2 for k >= 0.
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REFERENCES
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J. H. Conway and R. K. Guy, The Book of Numbers, Copernicus Press, NY, 1996. Sequence can be obtained by reading the successive circled numbers in the second display on page 64.
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LINKS
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FORMULA
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Let b=4. If n == -i (mod b) for 0 <= i < b, then a(n) = binomial(b,i+1)*((n+i)/b)^(i+1).
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MAPLE
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f:=proc(n, b) local i;
for i from 0 to b-1 do
if ((n+i) mod b) = 0 then return(binomial(b, i+1)*((n+i)/b)^(i+1)); fi;
od;
end;
[seq(f(n, 3), n=0..60)];
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PROG
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(Python)
from sympy import binomial
i = (4-n)%4
return binomial(4, i+1)*((n+i)//4)**(i+1) # Chai Wah Wu, Jul 25 2021
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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