A103334 Number of closed walks of length 2n at any of the nodes of degree 1 on the graph of the (7,4) Hamming code.

1, 1, 4, 24, 176, 1376, 10944, 87424, 699136, 5592576, 44739584, 357914624, 2863312896, 22906494976, 183251943424, 1466015514624, 11728124051456, 93824992280576, 750599937982464, 6004799503335424, 48038396025634816

Offset: 0

Author

Paul Barry, Jan 31 2005

Keywords

• easy
• nonn

Comments

a(n+1)=8^n/3+2^(n+1)/3 with g.f. (1-6x)/(1-10x+16x^2) counts walks of length 2n+1 between adjacent nodes of degrees 1 and 4 on the graph of the (7,4) Hamming code.

References

• David J.C. Mackay, Information Theory, Inference and Learning Algorithms, CUP, 2003, p. 19.

Links

• Index entries for linear recurrences with constant coefficients, signature (10,-16).

Crossrefs

Cf. A082412, A103333.

Formula

G.f.: (1-9x+10x^2)/(1-10x+16x^2); a(n)=8^(n-1)/3+2^(n)/3+5*0^n/8.