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 A024088 a(n) = 8^n-1. 7
 0, 7, 63, 511, 4095, 32767, 262143, 2097151, 16777215, 134217727, 1073741823, 8589934591, 68719476735, 549755813887, 4398046511103, 35184372088831, 281474976710655, 2251799813685247, 18014398509481983 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Numbers whose base 8 or octal representation is 777777.......7. - Zerinvary Lajos, Feb 03 2007 LINKS Index entries for linear recurrences with constant coefficients, signature (9,-8). FORMULA G.f.: 1/(1-8*x)-1/(1-x). [Mohammad K. Azarian, Jan 14 2009] E.g.f.: e^(8*x)-e^x. [Mohammad K. Azarian, Jan 14 2009] a(n) = A000225(n)*A001576(n). [Reinhard Zumkeller, Feb 15 2009] a(n) = 8*a(n-1)+7 for n>0, a(0)=0. [Vincenzo Librandi, Aug 03 2010] a(n) = Sum_{i=1..n} 7^i*binomial(n,n-i) for n>0, a(0)=0. [Bruno Berselli, Nov 11 2015] EXAMPLE a(1)=0+7=7; a(2)=8*7+7=63; a(3)=8*63+7=511. [Vincenzo Librandi, Aug 03 2010] MATHEMATICA 8^Range[0, 20]-1 (* or *) LinearRecurrence[{9, -8}, {0, 7}, 20] (* Harvey P. Dale, Jan 04 2017 *) PROG (Sage) [gaussian_binomial(3*n, 1, 2) for n in xrange(0, 19)] # Zerinvary Lajos, May 28 2009 (Sage) [stirling_number2(3*n+1, 2) for n in xrange(0, 19)] # Zerinvary Lajos, Nov 26 2009 (Sage) [8^n-1 for n in (0..20)] # Bruno Berselli, Nov 11 2015 CROSSREFS Sequence in context: A218633 A218283 A218237 * A155132 A270472 A266426 Adjacent sequences:  A024085 A024086 A024087 * A024089 A024090 A024091 KEYWORD nonn,easy AUTHOR STATUS approved

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