cp's OEIS Frontend

A329479 Number of degree n polynomials f with all nonzero coefficients equal to 1 such that f(k) is divisible by 3 for all integers k.

%I A329479 #25 Nov 18 2019 22:21:38
%S A329479 0,0,0,0,1,2,6,15,30,66,121,242,462,903,1806,3570,7225,14450,29070,
%T A329479 58311,116622,233586,466489,932978,1864590,3727815,7455630,14908530,
%U A329479 29822521,59645042,119301006,238612935,477225870,954473586,1908903481,3817806962,7635526542
%N A329479 Number of degree n polynomials f with all nonzero coefficients equal to 1 such that f(k) is divisible by 3 for all integers k.
%C A329479 Equivalently, this counts strings of numbers of length n that start with a 1 and which yield a multiple of 3 when read in any base.
%H A329479 Peter Kagey, <a href="/A329479/b329479.txt">Table of n, a(n) for n = 1..1000</a>
%F A329479 a(2n) = A024495(n-1) * A024493(n).
%F A329479 a(2n+1) = A024495(n) * A024493(n).
%F A329479 Conjectured recurrence: a(n) = 2a(n-1) + 2a(n-2) - 5a(n-3) - 2a(n-4) + 10a(n-5) - 4a(n-6) - 4a(n-7) + 8a(n-8).
%e A329479 For n = 7, the a(7) = 6 (0,1)-polynomials of degree seven such that f(0) = f(1) = f(2) = 0 (mod 3) are
%e A329479 x^7 + x^5 + x^3,
%e A329479 x^7 + x^6 + x^5 + x^4 + x^3 + x^2,
%e A329479 x^7 + x^5 + x,
%e A329479 x^7 + x^3 + x,
%e A329479 x^7 + x^6 + x^5 + x^4 + x^2 + x, and
%e A329479 x^7 + x^6 + x^4 + x^3 + x^2 + x.
%Y A329479 Cf. A024493, A024495, A329126.
%Y A329479 A008776(n) gives the number of polynomials of degree n+3 without the coefficient restriction.
%K A329479 nonn
%O A329479 1,6
%A A329479 _Peter Kagey_, Nov 13 2019