OFFSET
1,3
COMMENTS
A string and its reverse are considered to be equivalent. Permuting the colors will not change the structure.
REFERENCES
M. R. Nester (1999). Mathematical investigations of some plant interaction designs. PhD Thesis. University of Queensland, Brisbane, Australia. [See A056391 for pdf file of Chap. 2]
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 4).
FORMULA
a(n) = A005418(n) - 1.
From Colin Barker, Nov 25 2012: (Start)
a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
G.f.: x^2*(x^2+x-1)/((x-1)*(2*x-1)*(2*x^2-1)). (End)
4*a(n) = 2^n -4 +2*A016116(n). - R. J. Mathar, Feb 06 2026
MATHEMATICA
Table[(StirlingS2[n, 2] + StirlingS2[Floor[n/2]+1, 2])/2, {n, 1, 30}] (* Robert A. Russell, Jan 29 2018 *)
LinearRecurrence[{3, 0, -6, 4}, {0, 1, 2, 5}, 35] (* or *)
Rest@ CoefficientList[Series[x^2*(x^2 + x - 1)/((x - 1) (2 x - 1) (2 x^2 - 1)), {x, 0, 35}], x] (* Michael De Vlieger, Jan 31 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
