A343952 Let f map (x, y) to (x+y, x*y). Start from (X, X) and iterate f n times. Then a(n) is the coefficient of X^n in the polynomial in X that expresses the x-coordinate of the obtained position.

0, 2, 1, 2, 4, 10, 24, 66, 176, 498, 1416, 4122, 12068, 35930, 107632, 325346, 989600, 3029914, 9323248, 28831066, 89525028, 279074634, 872958488, 2739387258, 8621086800, 27203628682, 86050008056, 272807862746, 866704248868, 2758862542482, 8797833793728

Offset

0,2

Comments

a(n) is also the coefficient of X^n in the polynomial that expresses the x-coordinate after N iterations, for any N greater than n.

Links

Table of n, a(n) for n=0..30.

Example

Pos. 0: (                                        X+[0], X)
Pos. 1: (                                    [2]*X    , X^2)
Pos. 2: (                          [1]*X^2 +  2 *X    , 2*X^3)
Pos. 3: (                 [2]*X^3 + 1 *X^2 +  2 *X    , 2*X^5+4*X^4)
Pos. 4: (2*X^5 + [4]*X^4 + 2 *X^3 + 1 *X^2 +  2 *X    , 4*X^8+10*X^7+8*X^6+8*X^5)

Prog

(PARI)
list_a(nmax)= {
  my(n=0, v=[Ser(x, x, nmax), Ser(x, x, nmax)], f=v->[v[1]+v[2], v[1]*v[2]]); print1("0, ");
  while(n<nmax, n++; v=f(v); print1(polcoeff(v[1], n), ", "))}
list_a(30)

Crossrefs

Cf. A000045 (degree of the n-th x-coordinate polynomial).

Sequence in context: A029728 A135547 A146307 * A063894 A268619 A024500

Adjacent sequences: A343949 A343950 A343951 * A343953 A343954 A343955

Keyword

nonn

Author

Luc Rousseau, May 05 2021

Status

approved