OFFSET
1,3
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Kirchhoff Index.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,4,0,0,0,-6,0,0,0,4,0,0,0,-1).
FORMULA
a(n+2) = numerator of A000295(n+2)/(3*Integral_{t=0..2} t^n*(1-abs(1-t))^2).
a(n) = (n*(n-1)*(n+1)*(5+((-1)^n-(-1)^((2*n-1+(-1)^n)/4)-(-1)^((6*n-1+(-1)^n)/4))))/48. - Luce ETIENNE, Feb 17 2015
G.f.: x^2*(x^12 +2*x^11 +5*x^10 +10*x^9 +31*x^8 +20*x^7 +22*x^6 +20*x^5 +31*x^4 +10*x^3 +5*x^2 +2*x +1) / ((x -1)^4*(x +1)^4*(x^2 +1)^4). - Colin Barker, Feb 17 2015
Sum_{n>=2} 1/a(n) = 3 * (1 - log(2)/2). - Amiram Eldar, Aug 11 2022
EXAMPLE
0, 1/2, 2, 5, 10, 35/2, 28, 42, 60, 165/2, 110, 143, 182, ...
MATHEMATICA
Table[(n^3-n)/12, {n, 50}]//Numerator (* or *) LinearRecurrence[{0, 0, 0, 4, 0, 0, 0, -6, 0, 0, 0, 4, 0, 0, 0, -1}, {0, 1, 2, 5, 10, 35, 28, 42, 60, 165, 110, 143, 182, 455, 280, 340}, 50] (* Harvey P. Dale, Nov 05 2021 *)
PROG
(PARI) a(n) = numerator((n-1)*n*(n+1)/12); \\ Michel Marcus, Feb 17 2015
(PARI) a(n)=binomial(n+1, 3)/if(n%4==2, 1, 2) \\ Charles R Greathouse IV, Feb 17 2015
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
Eric W. Weisstein, Mar 04 2008
STATUS
approved