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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
 0, 1, 3, 7, 16, 38, 92, 220, 512, 1160, 2576, 5648, 12288, 26592, 57280, 122816, 262144, 557184, 1179904, 2490624, 5242880, 11009536, 23067648, 48233472, 100663296, 209717248, 436211712, 905973760, 1879048192, 3892305920, 8053047296, 16642981888, 34359738368 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Related to Clifford algebras (see A323100 and A323346). LINKS FORMULA a(n) = Sum_{k=0..n} A323346(n - k, k - 1). a(n) = (A001787(n) + A009545(n))/2. a(n) = [x^n] (x*(3*x^2 - 3*x + 1))/((2*x - 1)^2*(2*x^2 - 2*x + 1)). a(n) = n! [x^n] (exp(2*x)*x + exp(x)*sin(x))/2. a(n) = (4*n*a(n-3) + (2 - 6*n)*a(n-2) + (4*n - 2)*a(n-1))/(n - 1) for n >= 3. MAPLE a := n -> ((2^n*n + I*(1 - I)^n - I*(1 + I)^n))/4: seq(a(n), n=0..32); MATHEMATICA LinearRecurrence[{6, -14, 16, -8}, {0, 1, 3, 7}, 40] (* Jean-François Alcover, Mar 20 2019 *) CROSSREFS Antidiagonal sums of A323346. Cf. A001787, A009545, A321959, A323100. Sequence in context: A052967 A297498 A239040 * A293065 A211278 A196154 Adjacent sequences:  A323222 A323223 A323224 * A323226 A323227 A323228 KEYWORD nonn,easy AUTHOR Peter Luschny, Mar 18 2019 STATUS approved

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Last modified August 23 13:53 EDT 2019. Contains 326227 sequences. (Running on oeis4.)