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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
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.
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: A376989 A135547 A146307 * A063894 A268619 A024500
KEYWORD
nonn
AUTHOR
Luc Rousseau, May 05 2021
STATUS
approved