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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. 2
0, 0, 0, 0, 1, 2, 6, 15, 30, 66, 121, 242, 462, 903, 1806, 3570, 7225, 14450, 29070, 58311, 116622, 233586, 466489, 932978, 1864590, 3727815, 7455630, 14908530, 29822521, 59645042, 119301006, 238612935, 477225870, 954473586, 1908903481, 3817806962, 7635526542 (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 3 when read in any base.

LINKS

Peter Kagey, Table of n, a(n) for n = 1..1000

FORMULA

a(2n) = A024495(n-1) * A024493(n).

a(2n+1) = A024495(n) * A024493(n).

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).

EXAMPLE

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

x^7 + x^5 + x^3,

x^7 + x^6 + x^5 + x^4 + x^3 + x^2,

x^7 + x^5 + x,

x^7 + x^3 + x,

x^7 + x^6 + x^5 + x^4 + x^2 + x, and

x^7 + x^6 + x^4 + x^3 + x^2 + x.

CROSSREFS

Cf. A024493, A024495, A329126.

A008776(n) gives the number of polynomials of degree n+3 without the coefficient restriction.

Sequence in context: A289102 A289402 A289458 * A236111 A230455 A141126

Adjacent sequences:  A329476 A329477 A329478 * A329480 A329481 A329482

KEYWORD

nonn

AUTHOR

Peter Kagey, Nov 13 2019

STATUS

approved

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Last modified September 30 00:37 EDT 2020. Contains 337432 sequences. (Running on oeis4.)