OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,1,2).
FORMULA
a(n) = a(n-1) + a(n-5) + a(n-6) + 2*a(n-7) + delta(n,0) + delta(n,1) + 2*delta(n,2) + 4*delta(n,3) + 4*delta(n,4) + 3*delta(n,5) + 2*delta(n,6).
G.f.: (1 + x + 2*x^2 + 4*x^3 + 4*x^4 + 3*x^5 + 2*x^6)/(1 - x - x^5 - x^6 - 2*x^7).
EXAMPLE
When n = 5, the 16 subsets are {}, {1}, {2}, {3}, {4}, {5}, {1,2}, {1,3}, {2,3}, {2,4}, {3,4}, {3,5}, {4,5}, {1,2,3}, {2,3,4}, and {3,4,5}.
MATHEMATICA
CoefficientList[Series[(1 + x + 2x^2 + 4x^3 + 4x^4 + 3x^5 + 2x^6)/(1 - x - x^5 - x^6 - 2*x^7), {x, 0, 35}], x]
LinearRecurrence[{1, 0, 0, 0, 1, 1, 2}, {1, 2, 4, 8, 12, 16, 21}, 50] (* Harvey P. Dale, Mar 01 2023 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Michael A. Allen, Feb 22 2022
STATUS
approved