OFFSET
0,2
COMMENTS
a(n-4) for n>3 is the number of equivalence classes of binary words of length n for the subword 100110 (see A317669 for further explanation).
a(n) is the number of compositions of n+5 into parts 1, 6, 9, 12, 15, 18, ...
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,1).
FORMULA
a(n) = a(n-1) + a(n-3) - a(n-4) + a(n-6) for n>= 6.
G.f.: (1 + x + x^2 + x^4 + x^5)/(1 - x - x^3 + x^4 - x^6).
EXAMPLE
For n = 6, the 10 subsets are {}, {1}, {2}, {3}, {4}, {1,4}, {5}, {2,5}, {6}, {3,6}.
MATHEMATICA
CoefficientList[Series[(1 + x + x^2 + x^4 + x^5)/(1 - x - x^3 + x^4 - x^6), {x, 0, 42}], x]
LinearRecurrence[{1, 0, 1, -1, 0, 1}, {1, 2, 3, 4, 6, 8}, 42]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Michael A. Allen, Aug 02 2024
STATUS
approved