OFFSET
1,3
COMMENTS
These are possible sizes for 3-symmetric graphs.
The possible size of 2-symmetric graphs is sequence A042948.
These numbers are 0, 1, 2, 8, and 10 modulo 16.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).
FORMULA
G.f.: (6*x^4+2*x^3+6*x^2+x+1)*x^2/(x^6-x^5-x+1). - Alois P. Heinz, Nov 29 2019
a(n) = a(n-1) + a(n-5) - a(n-6) for n>6. - Colin Barker, Nov 29 2019
EXAMPLE
binomial(10, 3) = 120, which is divisible by 8. Thus 10 belongs to this sequence.
MATHEMATICA
Select[Range[200], Mod[Floor[#(#-1)(#-2)/6], 8]==0&] (* Joshua Oliver, Nov 26 2019 *)
LinearRecurrence[{1, 0, 0, 0, 1, -1}, {0, 1, 2, 8, 10, 16}, 80] (* Harvey P. Dale, Jul 03 2022 *)
PROG
(Python)
for n in range(200):
if (n*(n-1)*(n-2)//6)%8==0:
print(n, end=' ')
(PARI) for(k=0, 194, my(j=binomial(k, 3)); if(!(j%8), print1(k, ", "))) \\ Hugo Pfoertner, Nov 29 2019
(PARI) concat(0, Vec(x^2*(1 + x + 6*x^2 + 2*x^3 + 6*x^4) / ((1 - x)^2*(1 + x + x^2 + x^3 + x^4)) + O(x^70))) \\ Colin Barker, Nov 29 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Sebastian Jeon and Tanya Khovanova, Nov 25 2019
STATUS
approved