

A192023


The Wiener index of the combshaped graph __..._ with 2n (n>=1) nodes. The Wiener index of a connected graph is the sum of the distances between all unordered pairs of vertices in the graph.


3



1, 10, 31, 68, 125, 206, 315, 456, 633, 850, 1111, 1420, 1781, 2198, 2675, 3216, 3825, 4506, 5263, 6100, 7021, 8030, 9131, 10328, 11625, 13026, 14535, 16156, 17893, 19750, 21731, 23840, 26081, 28458, 30975, 33636, 36445, 39406, 42523, 45800, 49241, 52850, 56631
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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(n2) 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) / (x1)^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*n5) end proc: seq(a(n), n = 1 .. 43);


PROG

(MAGMA) [n*(2*n^2+6*n5)/3: n in [1..50]]; // Vincenzo Librandi, Jul 04 2011


CROSSREFS

Cf. A192022.
Sequence in context: A085473 A051943 A059306 * A219693 A297507 A283846
Adjacent sequences: A192020 A192021 A192022 * A192024 A192025 A192026


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, Jun 24 2011


STATUS

approved



