0,3

a(n)=A001045(n)*A011782(n) - Paul Barry (pbarry(AT)wit.ie), May 20 2003

The sequence 1,2,12,... is the binomial transform of (1,1,9,9,81,81,...)=2*3^n/3+(-3)^n/3 - Paul Barry (pbarry(AT)wit.ie), Jul 17 2003

Number of spanning trees in K_2 X P_n.

Form a graph whose adjacency matrix is the tensor product of that of C_3 and [1,1;1,1]. a(n) counts walks of length n between any pair of adjacent nodes. A054881(n) counts closed walks of length n at a node.

Arises in connection with merit factor of the GRS sequences - see Hoeholdt et al.

M. Gardner, Riddles of the Sphinx, New Mathematical Library, M.A.A., 1987, p. 145. Math. Rev. 89i:00015.

T. Hoeholdt, H. E. Jensen and J.Justesen, Aperiodic correlations and the merit factor of a class of binary sequences, IEEE Trans. Inform. Theory, 13 (1985), 549-552.

F. Faase, Counting Hamilton cycles in product graphs

Eric Weisstein's World of Mathematics, Octahedral Graph

a(1) = 1, a(2) = 2; a(n) = 2a(n-1) + 8a(n-2). - Barry E. Williams, Jan 04 2000

G.f.: x/((1+2x)(1-4x)).

a(n)=((1+3)^n-(1-3)^n)/6. - Paul Barry (pbarry(AT)wit.ie), May 14 2003

a(n)=sum{k=0..floor(n/2), C(n, 2k+1)9^k } - Paul Barry (pbarry(AT)wit.ie), May 20 2003

E.g.f.: exp(x)sinh(3x)/3 - Paul Barry (pbarry(AT)wit.ie), Jul 09 2003

(PARI) a(n)=if(n<0, 0, 2^(n-1)*(2^n-(-1)^n)/3)

a(n)=A003674(n)/3.

Sequence in context: A013194 A074447 A110953 this_sequence A098519 A127725 A048014

Adjacent sequences: A003680 A003681 A003682 this_sequence A003684 A003685 A003686

nonn

njas