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A279196 Number of polynomials P(x,y) with nonnegative integer coefficients such that P(x,y) == 1 (mod x+y-1) and P(1,1) = n. 0
1, 1, 2, 5, 13, 36, 102, 295, 864 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..9.

R. K. Guy, Letter to N. J. A. Sloane, June 24 1971: front, back [Annotated scanned copy, with permission] See sequence "D".

N. J. A. Sloane, Winter Fruits: New Problems from OEIS, Dec. 2016 - Jan. 2017 (part 1), 2017-01-26, (discussion from 6:23-10:00).

N. J. A. Sloane, Winter Fruits: New Problems from the OEIS, Dec. 2016 - Jan. 2017 (slides)

EXAMPLE

From Peter Kagey, Feb 03 2017 (Start):

For n = 1 the a(1) = 1 solution is:

  1 = 0(x + y - 1) + 1.

For n = 2 the a(2) = 1 solution is:

  x + y = (x + y - 1) + 1.

For n = 3 the a(3) = 2 solutions are:

  xy + x + y^2 = (y + 1)(x + y - 1) + 1;

  xy + y + x^2 = (x + 1)(x + y - 1) + 1.

For n = 4 the a(4) = 5 solutions are:

  x^2 + y^2             = (x + y + 1)(x + y - 1) + 1;

  x^2y + x^2 + xy^2 + y = (xy + x + 1)(x + y - 1) + 1;

  x^2y + xy^2 + x + y^2 = (xy + y + 1)(x + y - 1) + 1;

  xy^2 + xy + x + y^3   = (y^2 + y + 1)(x + y - 1) + 1;

  x^3 + x^2y + xy + y   = (x^2 + x + 1)(x + y - 1) + 1.

(End)

CROSSREFS

Sequence in context: A046171 A022854 A116409 * A002844 A223096 A277996

Adjacent sequences:  A279193 A279194 A279195 * A279197 A279198 A279199

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane, Dec 15 2016

STATUS

approved

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Last modified October 20 12:47 EDT 2019. Contains 328257 sequences. (Running on oeis4.)