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A309846 Number of degree n polynomials f with all nonzero coefficients equal to 1 such that f(k) is divisible by 4 for all integers k. 0
0, 0, 0, 0, 1, 2, 6, 10, 20, 32, 64, 120, 256, 512, 1056, 2080, 4160, 8192, 16384, 32640, 65536, 131072 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

Equivalently, this counts strings of numbers of length n that start with a 1 and which yield a multiple of 4 when read in any base.

Conjecture: All terms are of the form 2^(n-5), 2^k*(2^(n-k-5) + 1), or 2^k*(2^(n-k-5) - 1) for some value of k.

LINKS

Table of n, a(n) for n=1..22.

EXAMPLE

For n = 7, the a(7) = 6 (0,1)-polynomials of degree seven such that f(0) == f(1) == f(2) == f(3) == 0 (mod 3) are

x^7 + x^6 + x^5 + x^4,

x^7 + x^6 + x^4 + x^3,

x^7 + x^6 + x^5 + x^2,

x^7 + x^5 + x^4 + x^2,

x^7 + x^6 + x^3 + x^2, and

x^7 + x^4 + x^3 + x^2.

CROSSREFS

Cf. A329126, A329479.

Sequence in context: A211982 A096338 A198381 * A309874 A317759 A014279

Adjacent sequences:  A309843 A309844 A309845 * A309847 A309848 A309849

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 18 2019

STATUS

approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)