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 A127985 a(n) = floor(2^n*(n/3 + 4/9)). 1
 0, 1, 4, 11, 28, 67, 156, 355, 796, 1763, 3868, 8419, 18204, 39139, 83740, 178403, 378652, 800995, 1689372, 3553507, 7456540, 15612131, 32622364, 68040931, 141674268, 294533347, 611436316, 1267611875, 2624702236, 5428361443 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 (corrected by Ray Chandler, Jan 19 2019) Wieb Bosma, Signed bits and fast exponentiation, J. Th. Nombres de Bordeaux, 13 no. 1 (2001), p. 27-41. Index entries for linear recurrences with constant coefficients, signature (4, -3, -4, 4). FORMULA a(n) = (n/3 + 4/9)*2^n - 1/2 + (-1)^n/18. a(1)=1, a(2)=4, a(3)=11, a(4)=28, a(n) = 4*a(n-1)-3*a(n-2)-4*a(n-3)+4*a(n-4). - Harvey P. Dale, May 15 2011 G.f.: x*(1-2*x^2)/((1-2*x)^2*(1-x^2)). - Harvey P. Dale, May 15 2011 MATHEMATICA Table[(n/3 + 4/9) 2^n - 1/2 + (-1)^n/18, {n, 1, 50}] LinearRecurrence[{4, -3, -4, 4}, {1, 4, 11, 28}, 50] (* Harvey P. Dale, May 15 2011 *) PROG (MAGMA) [(n/3 + 4/9)*2^n - 1/2 + (-1)^n/18: n in [1..40]]; // Vincenzo Librandi, May 26 2011 (PARI) a(n)=(n*3+4)<

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Last modified July 23 16:14 EDT 2019. Contains 325258 sequences. (Running on oeis4.)