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A323225 a(n) = ((2^n*n + i*(1 - i)^n - i*(1 + i)^n))/4, where i is the imaginary unit. 0

%I

%S 0,1,3,7,16,38,92,220,512,1160,2576,5648,12288,26592,57280,122816,

%T 262144,557184,1179904,2490624,5242880,11009536,23067648,48233472,

%U 100663296,209717248,436211712,905973760,1879048192,3892305920,8053047296,16642981888,34359738368

%N a(n) = ((2^n*n + i*(1 - i)^n - i*(1 + i)^n))/4, where i is the imaginary unit.

%C Related to Clifford algebras (see A323100 and A323346).

%F a(n) = Sum_{k=0..n} A323346(n - k, k - 1).

%F a(n) = (A001787(n) + A009545(n))/2.

%F a(n) = [x^n] (x*(3*x^2 - 3*x + 1))/((2*x - 1)^2*(2*x^2 - 2*x + 1)).

%F a(n) = n! [x^n] (exp(2*x)*x + exp(x)*sin(x))/2.

%F a(n) = (4*n*a(n-3) + (2 - 6*n)*a(n-2) + (4*n - 2)*a(n-1))/(n - 1) for n >= 3.

%p a := n -> ((2^n*n + I*(1 - I)^n - I*(1 + I)^n))/4:

%p seq(a(n), n=0..32);

%t LinearRecurrence[{6, -14, 16, -8}, {0, 1, 3, 7}, 40] (* _Jean-Fran├žois Alcover_, Mar 20 2019 *)

%Y Antidiagonal sums of A323346.

%Y Cf. A001787, A009545, A321959, A323100.

%K nonn,easy

%O 0,3

%A _Peter Luschny_, Mar 18 2019

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Last modified October 16 16:34 EDT 2019. Contains 328101 sequences. (Running on oeis4.)