OFFSET
1,2
COMMENTS
The Wiener polynomials of these graphs are given in A192022.
a(n) = Sum_{k>=1} A192022(n,k).
Conjecture: for n>2, A192023(n-2) is the number of 2 X 2 matrices with all terms in {1,2,...,n} and determinant 2n. - Clark Kimberling, Mar 31 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1)
FORMULA
a(n) = n*(2*n^2 + 6*n - 5)/3.
G.f.: -x*(-1 - 6*x + 3*x^2) / (x-1)^4. - R. J. Mathar, Jun 26 2011
EXAMPLE
a(2)=10 because in the graph |_| there are 3 pairs of nodes at distance 1, 2 pairs at distance 2, and 1 pair at distance 3 (3*1 + 2*2 + 1*3 = 10).
MAPLE
a := proc (n) options operator: arrow: (1/3)*n*(2*n^2+6*n-5) end proc: seq(a(n), n = 1 .. 43);
PROG
(Magma) [n*(2*n^2+6*n-5)/3: n in [1..50]]; // Vincenzo Librandi, Jul 04 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Jun 24 2011
STATUS
approved