OFFSET
1,1
LINKS
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 (37,-549,4185,-17523,40095,-45927,19683).
FORMULA
a(n) = -(7/8)+3^n*(2*n^2-(9/4)*n-10)+3^(2*n)*(4*n^2-(41/4)*n+(87/8)).
G.f.: x*(243*x^4+3807*x^3-369*x^2-87*x-10) / ((x-1)*(3*x-1)^3*(9*x-1)^3). [Colin Barker, Jan 01 2013]
MAPLE
a := proc (n) options operator, arrow: -7/8+3^n*(2*n^2-(9/4)*n-10)+3^(2*n)*(4*n^2-(41/4)*n+87/8) end proc: seq(a(n), n = 1 .. 18);
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Dec 30 2012
EXTENSIONS
Offset changed from 0 to 1 by Bruno Berselli, Dec 30 2012
STATUS
approved