OFFSET
1,2
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..200
EXAMPLE
Given x/(1-x+x^2) = x + x^2 - x^4 - x^5 + x^7 + x^8 - x^10 - x^11 + x^13 +...
form a table of coefficients in the iterations of x/(1-x+x^2) like so:
[1, 1, 0, -1, -1, 0, 1, 1, 0, -1, ...];
[1, 2, 2, -1, -8, -15, -10, 22, 79, 112, ...];
[1, 3, 6, 6, -11, -73, -201, -309, 37, 1913, ...];
[1, 4, 12, 26, 24, -116, -808, -3000, -7566, -9882, ...];
[1, 5, 20, 65, 155, 120, -1379, -10761, -51202, -183269, ...];
[1, 6, 30, 129, 464, 1225, 702, -18978, -169139, -994138, ...];
[1, 7, 42, 224, 1057, 4235, 12411, 4445, -301321, -3076795, ...];
[1, 8, 56, 356, 2064, 10752, 48000, 156416, 27812, -5458012, ...];
[1, 9, 72, 531, 3639, 23064, 132633, 658197, 2388060, 187911, ...];
[1, 10, 90, 755, 5960, 44265, 306742, 1942198, 10676571, 43159172, ...]; ...
then this sequence forms the main diagonal in the above table.
PROG
(PARI) {a(n)=local(A=x, G=x/(1-x+x^2)); for(i=1, n, A=subst(G, x, A+x*O(x^(n)))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 17 2014
STATUS
approved