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A383953
a(0) = 4, a(n) = 2*a(n-1) + (-1)^n.
0
4, 7, 15, 29, 59, 117, 235, 469, 939, 1877, 3755, 7509, 15019, 30037, 60075, 120149, 240299, 480597, 961195, 1922389, 3844779, 7689557, 15379115, 30758229, 61516459, 123032917, 246065835, 492131669, 984263339, 1968526677, 3937053355, 7874106709, 15748213419, 31496426837
OFFSET
0,1
FORMULA
a(n) = (11*2^n + (-1)^n)/3.
a(n) = A340627(n+1)/2.
a(n) = 2*A052997(n) + 1 for n >= 1.
a(n) = 11*A001045(n) + (-1)^n*4.
a(n) = a(n-4) + 55*2^(n-4) for n >= 4.
G.f.: (3*x + 4)/((x + 1)*(1 - 2*x)).
E.g.f: (11*exp(2*x) + exp(-x))/3.
MATHEMATICA
a[n_] := (11*2^n + (-1)^n)/3; Array[a, 34, 0] (* Amiram Eldar, Aug 20 2025 *)
CROSSREFS
Bisections give A199210 and A072261.
Sequence in context: A301204 A116969 A131090 * A178615 A131935 A119749
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Aug 19 2025
STATUS
approved