OFFSET
1,2
COMMENTS
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
G.f.: x^2*(8 + x)/((1 + x)*(1 - x)^2).
a(n) = (18*n + 7*(-1)^n - 11)/4. Therefore: a(2*m) = 9*m-1, a(2*m+1) = 9*m. It follows that a(j)+a(k) and a(j)*a(k) belong to the sequence if j and k are not both even.
a(n) = -A090570(-n+2).
a(n) = a(n-1) + a(n-2) - a(n-3).
a(2*r+1) + a(2*r+s+1) = a(4*r+s+1) and a(2*r) + a(2*r+2*s+1) = a(4*r+2*s). A particular case provided by these identities: a(n) = a(n - 2*floor(n/6)) + a(2*floor(n/6) + 1).
E.g.f.: 1 + ((9*x - 2)*cosh(x) + 9*(x - 1)*sinh(x))/2. - Stefano Spezia, Apr 24 2021
MATHEMATICA
Select[Range[0, 300], Divisible[# (# + 1), 9] &]
PROG
(PARI) for(n=0, 300, if(n*(n+1)%9==0, print1(n", ")))
(Sage) [n for n in range(300) if 9.divides(n*(n+1))]
(Magma) [n: n in [0..300] | IsDivisibleBy(n*(n+1), 9)];
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Jun 20 2016
STATUS
approved