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%I #12 Feb 06 2019 02:00:43
%S 1,3,9,22,50,113,256,576,1281,2818,6146,13313,28672,61440,131073,
%T 278530,589826,1245185,2621440,5505024,11534337,24117250,50331650,
%U 104857601,218103808,452984832,939524097,1946157058,4026531842,8321499137,17179869184,35433480192
%N A007318 * A143097.
%C A143100 = (1, 3, 4, 6, 13, 30, 64, 129, ...).
%H Nathaniel Johnston, <a href="/A143099/b143099.txt">Table of n, a(n) for n = 1..1000</a>
%F Binomial transform of A143097: (1, 2, 4, 3, 5, 7, 6, 8, 10, 9, 11, ...). a(n) = 2*a(n-1) + A143100(n-1).
%F G.f.: x*(5*x^4-7*x^3+5*x^2-3*x+1)/((1-x)*(x^2-x+1)*(1-2*x)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; [corrected by _R. J. Mathar_, Sep 16 2009]
%e a(4) = 22 = (1, 3, 3, 1) dot (1, 2, 4, 3) = (1 + 6 + 12 + 3).
%e a(4) = 22 = 2*a(3) + A143099(3) = 2*9 + 4, where 4 = A143100(3).
%p A143097 := proc(n) if(n<=1)then return n: elif(n mod 3 <= 1)then return n+1-2*(n mod 3): else return n: fi: end: A143099 := proc(n) return add(binomial(n-1,k-1)*A143097(k),k=1..n): end: seq(A143099(n),n=1..32); # _Nathaniel Johnston_, Apr 30 2011
%Y Cf. A143097, A143098, A143100.
%K nonn,easy
%O 1,2
%A _Gary W. Adamson_, Jul 24 2008
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