OFFSET
0,3
COMMENTS
A row of triangle A051168.
LINKS
Pedro Antonio, Table of n, a(n) for n = 0..100
Index entries for linear recurrences with constant coefficients, signature (6, -15, 23, -33, 51, -64, 63, -63, 64, -51, 33, -23, 15, -6, 1).
FORMULA
a(n) = (1/(n+9))*Sum_{d divides gcd(n+9,9)} mu(d)*binomial((n+9)/d, 9/d).
G.f.: (x*(x^4-x^3+3*x^2-x+1))/((x^2+x+1)^3*(1-x)^9).
G.f.: ((-1+x^3)^-3-(-1+x)^-9)/9. - Herbert Kociemba, Oct 16 2016
MATHEMATICA
CoefficientList[Series[(x (x^4 - x^3 + 3*x^2 - x + 1))/((x^2 + x + 1)^3 (1 - x)^9), {x, 0, 40}], x] (* Wesley Ivan Hurt, Oct 15 2015 *)
CoefficientList[Series[((-1+x^3)^-3-(-1+x)^-9)/9, {x, 0, 40}], x] (* Herbert Kociemba, Oct 16 2016 *)
LinearRecurrence[{6, -15, 23, -33, 51, -64, 63, -63, 64, -51, 33, -23, 15, -6, 1}, {0, 1, 5, 18, 55, 143, 333, 715, 1430, 2700, 4862, 8398, 13995, 22610, 35530}, 40] (* Harvey P. Dale, Feb 10 2023 *)
PROG
(PARI) a(n)= (1/(n+9))*sumdiv(gcd(n+9, 9), d, moebius(d)*binomial( (n+9)/d , 9/d )); \\ Michel Marcus, Oct 14 2015
(Python)
from sympy import mobius, binomial, gcd, divisors
print([sum(mobius(d) * binomial((n + 9)//d, 9//d) for d in divisors(gcd(n + 9, 9))) // (n + 9) for n in range(51)]) # Indranil Ghosh, Mar 26 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Criel Merino, Pedro Antonio, Oct 14 2015
EXTENSIONS
More terms from Michel Marcus, Oct 14 2015
STATUS
approved