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A270797
a(n) = J(n) if n odd, or 4*J(n) if n even, where J = Jacobsthal numbers A001045.
1
0, 1, 4, 3, 20, 11, 84, 43, 340, 171, 1364, 683, 5460, 2731, 21844, 10923, 87380, 43691, 349524, 174763, 1398100, 699051, 5592404, 2796203, 22369620, 11184811, 89478484, 44739243, 357913940, 178956971, 1431655764, 715827883, 5726623060, 2863311531, 22906492244
OFFSET
0,3
LINKS
H. Bruhn, L. Gellert, J. Günther, Jacobsthal numbers in generalised Petersen graphs, arXiv preprint arXiv:1503.03390 [math.CO], 2015.
H. Bruhn, L. Gellert, J. Günther, Jacobsthal numbers in generalised Petersen graphs, Electronic Notes in Discrete Math., 2015.
FORMULA
From Colin Barker, Apr 01 2016: (Start)
a(n) = (-3+3*(-2)^n-5*(-1)^n+5*2^n)/6.
a(n) = (2^(n+3)-8)/6 for n even.
a(n) = (2^(n+1)+2)/6 for n odd.
a(n) = 5*a(n-2)-4*a(n-4) for n>3.
G.f.: x*(1+4*x-2*x^2) / ((1-x)*(1+x)*(1-2*x)*(1+2*x)).
(End)
PROG
(PARI) concat(0, Vec(x*(1+4*x-2*x^2)/((1-x)*(1+x)*(1-2*x)*(1+2*x)) + O(x^50))) \\ Colin Barker, Apr 01 2016
CROSSREFS
Cf. A001045.
Sequence in context: A278424 A278662 A220861 * A280615 A281042 A076589
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Mar 31 2016
STATUS
approved