A192858 Hosoya indices of the 2n-wheel graphs W_{2n}.

2, 10, 36, 120, 382, 1178, 3550, 10514, 30720, 88788, 254342, 723190, 2043386, 5742490, 16062492, 44744688, 124192270, 343594514, 947857750, 2608015778, 7159034232, 19609583820, 53608363286, 146290947310, 398552156402, 1084153113898, 2944982283540, 7989231439464, 21646950044830, 58585895022218, 158389325993422

Offset: 1

Author

Eric W. Weisstein, Jul 11 2011

Keywords

• nonn
• easy

Comments

Wheel graphs are defined for n >= 4; extended to n=2 using recurrence.

Binomial transform of A120940 multiplied by 2. - R. J. Mathar, Jul 11 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Hosoya Index
• Eric Weisstein's World of Mathematics, Wheel Graph
• Index entries for linear recurrences with constant coefficients, signature (6,-11,6,-1)

Programs

Magma

I:=[2,10,36,120]; [n le 4 select I[n] else 6*Self(n-1)-11*Self(n-2)+6*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Aug 31 2011

Mathematica

LinearRecurrence[{6, -11, 6, -1}, {10, 36, 120, 382}, {0, 30}]

PARI

x='x+O('x^30); Vec(2*x*(1+x)*(x-1)^2/((x^2-3*x+1)^2)) \\ G. C. Greubel, Nov 10 2018

Formula

a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) - a(n-4).

G.f.: 2*x*(1+x)*(x-1)^2 / ( (x^2 - 3*x + 1)^2 ). - R. J. Mathar, Jul 11 2011

a(n) = ((3+r)^n*((5-r)*n+3*r-5) + (3-r)^n*((5+r)*n-3*r-5))/(5*2^n) with r=sqrt(5). - Bruno Berselli, Aug 31 2011

a(n) = 2*A377857(n+2). - R. J. Mathar, Dec 16 2024