OFFSET
1,1
COMMENTS
The flower graph is defined for n >= 5. Sequence extended to n = 1 using the formula.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Flower Graph.
Eric Weisstein's World of Mathematics, Minimum Total Dominating Set.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
FORMULA
a(n) = 3*a(n-4) - 3*a(n-8) + a(n-12).
G.f.: -3*x*(1+3*x+3*x^2+12*x^3+2*x^4+18*x^5-2*x^6-24*x^7-3*x^8+3*x^9-x^10+12*x^11)/(x-1)^3/(1+x)^3/(x^2+1)^3. - R. J. Mathar, Apr 02 2025
MATHEMATICA
Table[Piecewise[{{36, Mod[n, 4] == 0}, {3 n, Mod[n, 2] == 1}, {9 n^2/4, Mod[n, 4] == 2}}], {n, 20}]
LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {3, 9, 9, 36, 15, 81, 21, 36, 27, 225, 33, 36}, 20]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 30 2025
EXTENSIONS
a(41) onward from Andrew Howroyd, Nov 07 2025
STATUS
approved