OFFSET
1,1
LINKS
Ray Chandler, Table of n, a(n) for n = 1..1000
K. Balasubramanian, Recent developments in tree-pruning methods and polynomials for cactus graphs and trees, J. Math. Chemistry, 4 (1990) 89-102.
H. Hosoya and K. Balasubramanian, Exact dimer statistics and characteristic polynomials of cacti lattices, Theor. Chim. Acta 76 (1989) 315-329. Also on ResearchGate.
Index entries for linear recurrences with constant coefficients, signature (25, -222, 846, -1377, 729).
FORMULA
a(n) = -(1/2)+3^n*(n+5)+3^(2*n)*(3*n-(9/2)).
G.f.: 4*x*(1+21*x-54*x^2)/((1-x)*(1-3*x)^2*(1-9*x)^2). - Bruno Berselli, Dec 30 2012
MAPLE
a := proc (n) options operator, arrow: -1/2+3^n*(n+5)+3^(2*n)*(3*n-9/2) end proc: seq(a(n), n = 1 .. 20);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Dec 30 2012
STATUS
approved