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 A140991 a(n) = (1/9)*(7*2^n + (-1)^n*(3*n+2)) - (n-1)^2. 0
 0, 1, 3, 1, 5, 7, 27, 61, 153, 331, 719, 1489, 3069, 6223, 12579, 25285, 50753, 101683, 203607, 407449, 815205, 1630711, 3261803, 6523981, 13048425, 26097307, 52195167, 104390881, 208782413, 417565471, 835131699, 1670264149 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics, Addison-Wesley, Reading, MA, 1990, p. 327. LINKS Table of n, a(n) for n=0..31. Index entries for linear recurrences with constant coefficients, signature (3, 0, -6, 3, 3, -2). FORMULA a(n) = A006904(n) - (n-1)^2. From R. J. Mathar, Mar 27 2009: (Start) a(n) = 3*a(n-1) - 6*a(n-3) + 3*a(n-4) + 3*a(n-5) - 2*a(n-6). G.f.: x*(1-8*x^2+8*x^3+7*x^4)/((-1+2*x)*(1+x)^2*(x-1)^3). (End) EXAMPLE a(0) = (1/9)*(7*2^0 + (-1)^0*(3*0+2)) - (0-1)^2 = (1/9)*(7*1 + 1*(0+2)) - (-1)^2 = (1/9)*(7+2) - 1 = 1 - 1 = 0. PROG (Magma) [ (1/9)*(7*2^n+(-1)^n*(3*n+2))-(n-1)^2: n in [0..100] ]; // Vincenzo Librandi, Dec 19 2010 CROSSREFS Cf. A006904. Sequence in context: A049764 A136437 A137328 * A302191 A261712 A038738 Adjacent sequences: A140988 A140989 A140990 * A140992 A140993 A140994 KEYWORD nonn AUTHOR Juri-Stepan Gerasimov, Jul 08 2008 EXTENSIONS Definition corrected by D. S. McNeil, Mar 21 2009 STATUS approved

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Last modified July 18 06:32 EDT 2024. Contains 374377 sequences. (Running on oeis4.)