OFFSET
1,3
COMMENTS
Extended to a(1)-a(2) using the formula.
LINKS
Eric Weisstein's World of Mathematics, Moebius Ladder.
Eric Weisstein's World of Mathematics, Upper Domination Number.
Eric Weisstein's World of Mathematics, Upper Irredundance Number.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
a(n) = (4*n + 2*cos(n*Pi/2) - 1 - (-1)^n)/4.
G.f.: x*(1+2*x^2+x^3)/((-1+x)^2*(1+x+x^2+x^3)).
a(n) = a(n-1)+a(n-4)-a(n-5).
E.g.f.: (cos(x) + (2*x - 1)*cosh(x) + 2*x*sinh(x))/2. - Stefano Spezia, Jan 17 2026
MATHEMATICA
Table[(4 n + 2 Cos[n Pi/2] - 1 - (-1)^n)/4, {n, 20}]
Table[4 + Floor[(n - 5)/4] + 2 Floor[(n - 3)/4] + Floor[n/4], {n, 20}]
LinearRecurrence[{1, 0, 0, 1, -1}, {1, 1, 3, 4, 5}, 20]
CoefficientList[Series[(1 + 2 x^2 + x^3)/((-1 + x)^2 (1 + x + x^2 + x^3)), {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jan 17 2026
STATUS
approved
