This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A159741 #32 Jun 16 2025 00:47:07
%S A159741 8,24,56,120,248,504,1016,2040,4088,8184,16376,32760,65528,131064,
%T A159741 262136,524280,1048568,2097144,4194296,8388600,16777208,33554424,
%U A159741 67108856,134217720,268435448,536870904,1073741816,2147483640,4294967288,8589934584,17179869176,34359738360
%N A159741 a(n) = 8*(2^n - 1).
%C A159741 Fifth diagonal of the array which contains m-acci numbers in the m-th row.
%C A159741 The base array is constructed from m-acci numbers starting each with 1, 1, and 2 and filling one row of the table (see the examples).
%C A159741 The main and the upper diagonals of the table are the powers of 2, A000079.
%C A159741 The first subdiagonal is essentially A000225, followed by essentially A036563.
%C A159741 The next subdiagonal is this sequence here, followed by A159742, A159743, A159744, A159746, A159747, A159748.
%C A159741 a(n) written in base 2: 1000, 11000, 111000, 1111000, ..., i.e., n times 1 and 3 times 0 (A161770). - _Jaroslav Krizek_, Jun 18 2009
%C A159741 Also numbers for which n^8/(n+8) is an integer. - _Vicente Izquierdo Gomez_, Jan 03 2013
%H A159741 G. C. Greubel, <a href="/A159741/b159741.txt">Table of n, a(n) for n = 1..1000</a>
%H A159741 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A159741 From _R. J. Mathar_, Apr 22 2009: (Start)
%F A159741 a(n) = 3*a(n-1) - 2*a(n-2).
%F A159741 a(n) = 8*(2^n-1).
%F A159741 G.f.: 8*x/((2*x-1)*(x-1)). (End)
%F A159741 From _Jaroslav Krizek_, Jun 18 2009: (Start)
%F A159741 a(n) = Sum_{i=3..(n+2)} 2^i.
%F A159741 a(n) = Sum_{i=1..n} 2^(i+2).
%F A159741 a(n) = a(n-1) + 2^(n+2) for n >= 2. (End)
%F A159741 a(n) = A173787(n+3,3) = A175166(2*n)/A175161(n). - _Reinhard Zumkeller_, Feb 28 2010
%F A159741 From _Elmo R. Oliveira_, Jun 15 2025: (Start)
%F A159741 E.g.f.: 8*exp(x)*(exp(x) - 1).
%F A159741 a(n) = 8*A000225(n) = 4*A000918(n+1) = 2*A028399(n+2). (End)
%e A159741 From _R. J. Mathar_, Apr 22 2009: (Start)
%e A159741 The base table is
%e A159741 .1..1....1....1....1....1....1....1....1....1....1....1....1....1
%e A159741 .1..1....1....1....1....1....1....1....1....1....1....1....1....1
%e A159741 .2..2....2....2....2....2....2....2....2....2....2....2....2....2
%e A159741 .0..2....3....4....4....4....4....4....4....4....4....4....4....4
%e A159741 .0..2....5....7....8....8....8....8....8....8....8....8....8....8
%e A159741 .0..2....8...13...15...16...16...16...16...16...16...16...16...16
%e A159741 .0..2...13...24...29...31...32...32...32...32...32...32...32...32
%e A159741 .0..2...21...44...56...61...63...64...64...64...64...64...64...64
%e A159741 .0..2...34...81..108..120..125..127..128..128..128..128..128..128
%e A159741 .0..2...55..149..208..236..248..253..255..256..256..256..256..256
%e A159741 .0..2...89..274..401..464..492..504..509..511..512..512..512..512
%e A159741 .0..2..144..504..773..912..976.1004.1016.1021.1023.1024.1024.1024
%e A159741 .0..2..233..927.1490.1793.1936.2000.2028.2040.2045.2047.2048.2048
%e A159741 .0..2..377.1705.2872.3525.3840.3984.4048.4076.4088.4093.4095.4096
%e A159741 Columns: A000045, A000073, A000078, A001591, A001592 etc. (End)
%p A159741 T := proc(n,m) option remember ; if n < 0 then 0; elif n <= 1 then 1; elif n = 2 then 2; else add(procname(n-i,m),i=1..m) ; fi: end: A159741 := proc(n) T(n+4,n+1) ; end: seq(A159741(n),n=1..40) ; # _R. J. Mathar_, Apr 22 2009
%t A159741 Table[8(2^n-1),{n,60}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 18 2011 *)
%t A159741 LinearRecurrence[{3,-2},{8,24},30] (* _Harvey P. Dale_, Jan 01 2019 *)
%o A159741 (PARI) a(n)=8*(2^n-1) \\ _Charles R Greathouse IV_, Sep 24 2015
%o A159741 (Magma) [8*(2^n -1): n in [1..50]]; // _G. C. Greubel_, May 22 2018
%Y A159741 Cf. A000079, A000225, A036563, A159742, A159743, A159744, A159746, A159747, A159748.
%Y A159741 Cf. A000918, A028399, A161770, A173787, A175161, A175166.
%K A159741 nonn,easy
%O A159741 1,1
%A A159741 Al Hakanson (hawkuu(AT)gmail.com), Apr 20 2009
%E A159741 More terms from _R. J. Mathar_, Apr 22 2009
%E A159741 Edited by Al Hakanson (hawkuu(AT)gmail.com), May 11 2009
%E A159741 Comments claiming negative entries deleted by _R. J. Mathar_, Aug 24 2009