

A270438


a(n) is the number of entries == 1 mod 4 in row n of Pascal's triangle.


2



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

0,2


COMMENTS

All entries are powers of 2.


LINKS

Robert Israel, Table of n, a(n) for n = 0..10000
Kenneth S. Davis and William A. Webb, Pascal's triangle modulo 4, Fib. Quart., 29 (1991), 7983.
A. Granville, Zaphod Beeblebrox's Brain and the Fiftyninth Row of Pascal's Triangle, The American Mathematical Monthly, 99(4) (1992), 318331.


FORMULA

a(n) = 2^(A000120(n)  min(1, A014081(n))). [Davis & Webb]


EXAMPLE

Row 3 of Pascal's triangle is (1,3,3,1) and has two entries == 1 (mod 4), so a(3) = 2.


MAPLE

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^(m1) else 2^m fi
end proc:
map(f, [$0..1000]);


MATHEMATICA

Count[#, 1] & /@ Table[Mod[Binomial[n, k], 4], {n, 0, 120}, {k, 0, n}] (* Michael De Vlieger, Feb 26 2017 *)


PROG

(PARI) a(n) = 2^(hammingweight(n)  min(hammingweight(bitand(n, n>>1)), 1)) \\ Charles R Greathouse IV, Jul 13 2016


CROSSREFS

Cf. A034931, A163000, A000120, A007318, A014081.
Sequence in context: A318472 A186643 A286575 * A318836 A003036 A089818
Adjacent sequences: A270435 A270436 A270437 * A270439 A270440 A270441


KEYWORD

nonn,easy


AUTHOR

Robert Israel, Jul 12 2016


STATUS

approved



