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 A059672 Sum of binary numbers with n 1's and one (possibly leading) 0. 4
 0, 3, 14, 45, 124, 315, 762, 1785, 4088, 9207, 20470, 45045, 98292, 212979, 458738, 983025, 2097136, 4456431, 9437166, 19922925, 41943020, 88080363, 184549354, 385875945, 805306344, 1677721575, 3489660902, 7247757285, 15032385508 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n-1) is also the number of multiplications required to compute the permanent of general n X n matrices using Ryser's formula (see Kiah et al.). - Stefano Spezia, Oct 25 2021 REFERENCES Herbert John Ryser, Combinatorial Mathematics, volume 14 of Carus Mathematical Monographs. American Mathematical Soc., (1963), pp. 24-28. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Han Mao Kiah, Alexander Vardy and Hanwen Yao, Computing Permanents on a Trellis, arXiv:2107.07377 [cs.IT], 2021. See Table 1 p. 3. Index entries for linear recurrences with constant coefficients, signature (6,-13,12,-4). FORMULA a(n) = n*(2^(n+1)-1) = A058922(n+1) - n. G.f.: x*(3-4*x)/((1-x)^2*(1-2*x)^2). - Colin Barker, Mar 21 2012 a(n) = Sum_{k=0..n} Sum_{i=0..n} C(n+1,i) - C(k,i). - Wesley Ivan Hurt, Sep 21 2017 E.g.f.: x*exp(x)*(4*exp(x) - 1). - Stefano Spezia, Oct 25 2021 EXAMPLE a(4)=124 since the binary sum 11110+11101+11011+10111+01111 is 30+29+27+23+15. MATHEMATICA A059672[n_Integer] := n*(2^(n + 1) - 1); Table[A059672[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Jul 22 2011 *) LinearRecurrence[{6, -13, 12, -4}, {0, 3, 14, 45}, 40] (* Harvey P. Dale, Aug 30 2016 *) PROG (MAGMA) [n*(2^(n+1)-1): n in [0..35]]; // Vincenzo Librandi, Jul 23 2011 (PARI) a(n) =2*n<

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Last modified July 6 18:31 EDT 2022. Contains 355114 sequences. (Running on oeis4.)