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A270438
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a(n) is the number of entries == 1 mod 4 in row n of Pascal's triangle.
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2
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1, 2, 2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 2, 4, 4, 8, 2, 4, 4, 4, 4, 8, 4, 8, 2, 4, 4, 8, 4, 8, 8, 16, 2, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 2, 4, 4, 8, 4, 8, 8, 16, 4, 8, 8, 16, 8, 16, 16, 32, 2, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 4, 8, 8, 16, 4, 8, 8
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OFFSET
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0,2
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COMMENTS
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All entries are powers of 2.
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LINKS
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FORMULA
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EXAMPLE
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Row 3 of Pascal's triangle is (1,3,3,1) and has two entries == 1 (mod 4), so a(3) = 2.
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MAPLE
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f:= proc(n) local L, m;
L:= convert(n, base, 2);
m:= convert(L, `+`);
if has(L[1..-2]+L[2..-1], 2) then 2^(m-1) else 2^m fi
end proc:
map(f, [$0..1000]);
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MATHEMATICA
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Count[#, 1] & /@ Table[Mod[Binomial[n, k], 4], {n, 0, 120}, {k, 0, n}] (* Michael De Vlieger, Feb 26 2017 *)
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PROG
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(PARI) a(n) = 2^(hammingweight(n) - min(hammingweight(bitand(n, n>>1)), 1)) \\ Charles R Greathouse IV, Jul 13 2016
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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