A228322 The Wiener index of the graph obtained by applying Mycielski's construction to the hypercube graph Q(n) (n>=1).

15, 56, 232, 1008, 4432, 19328, 82944, 349952, 1454848, 5978112, 24352768, 98594816, 397479936, 1597865984, 6411452416, 25695289344, 102901940224, 411899002880, 1648290693120, 6594803793920, 26383058206720, 105541162500096, 422185252421632

Offset

1,1

References

D. B. West, Introduction to Graph Theory, 2nd ed., Prentice-Hall, NJ, 2001, p. 205.

Links

Table of n, a(n) for n=1..23.

R. Balakrishnan, S. F. Raj, The Wiener number of powers of the Mycielskian, Discussiones Math. Graph Theory, 30, 2010, 489-498 (see Theorem 2.1).

B. E. Sagan, Y-N. Yeh and P. Zhang, The Wiener Polynomial of a Graph, Internat. J. of Quantum Chem., 60, 1996, 959-969.

Index entries for linear recurrences with constant coefficients, signature (12,-56,128,-144,64).

Formula

a(n) = 6*2^(2*n) - 2^(n-2)*(4 + 12*n + n^2 + n^3).

G.f.: x*(15 - 124*x + 400*x^2 - 560*x^3 + 320*x^4)/((1 - 4*x)*(1 - 2*x)^4).

Example

a(1)=15 because Q(1) is the 1-edge path whose Mycielskian is the cycle graph C(5) with Wiener index 5*1+5*2 = 15.

Maple

a := proc (n) options operator, arrow: 6*2^(2*n)-2^(n-2)*(4+12*n+n^2+n^3) end proc: seq(a(n), n = 1 .. 25);

Mathematica

LinearRecurrence[{12, -56, 128, -144, 64}, {15, 56, 232, 1008, 4432}, 30] (* Harvey P. Dale, Mar 02 2019 *)

Crossrefs

Sequence in context: A250956 A243318 A304295 * A219630 A219849 A157856

Adjacent sequences: A228319 A228320 A228321 * A228323 A228324 A228325

Keyword

nonn,easy

Author

Emeric Deutsch, Aug 27 2013

Status

approved