A159741 a(n) = 8*(2^n - 1).

8, 24, 56, 120, 248, 504, 1016, 2040, 4088, 8184, 16376, 32760, 65528, 131064, 262136, 524280, 1048568, 2097144, 4194296, 8388600, 16777208, 33554424, 67108856, 134217720, 268435448, 536870904, 1073741816, 2147483640

Offset

1,1

Comments

Fifth diagonal of the array which contains m-acci numbers in the m-th row.

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.)

The main and the upper diagonals of the table are the powers of 2, A000079.

The first subdiagonal is essentially A000225, followed by essentially A036563.

The next subdiagonal is this sequence here, followed by A159742, A159743, A159744, A159746, A159747, A159748.

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

a(n) = A173787(n+3,3) = A175166(2*n)/A175161(n). - Reinhard Zumkeller, Feb 28 2010

Also numbers for which n^8/(n+8) is an integer. - Vicente Izquierdo Gomez, Jan 03 2013

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3, -2).

Formula

From R. J. Mathar, Apr 22 2009: (Start)

a(n) = 3*a(n-1) - 2*a(n-2).

a(n) = 8*(2^n-1).

G.f.: 8*x/((2*x-1)*(x-1)). (End)

From Jaroslav Krizek, Jun 18 2009: (Start)

a(n) = Sum_{i=3..(n+2)} 2^i.

a(n) = Sum_{i=1..n} 2^(i+2).

a(n) = a(n-1) + 2^(n+2) for n >= 2. (End)

Example

From R. J. Mathar, Apr 22 2009: (Start)
The base table is
.1..1....1....1....1....1....1....1....1....1....1....1....1....1
.1..1....1....1....1....1....1....1....1....1....1....1....1....1
.2..2....2....2....2....2....2....2....2....2....2....2....2....2
.0..2....3....4....4....4....4....4....4....4....4....4....4....4
.0..2....5....7....8....8....8....8....8....8....8....8....8....8
.0..2....8...13...15...16...16...16...16...16...16...16...16...16
.0..2...13...24...29...31...32...32...32...32...32...32...32...32
.0..2...21...44...56...61...63...64...64...64...64...64...64...64
.0..2...34...81..108..120..125..127..128..128..128..128..128..128
.0..2...55..149..208..236..248..253..255..256..256..256..256..256
.0..2...89..274..401..464..492..504..509..511..512..512..512..512
.0..2..144..504..773..912..976.1004.1016.1021.1023.1024.1024.1024
.0..2..233..927.1490.1793.1936.2000.2028.2040.2045.2047.2048.2048
.0..2..377.1705.2872.3525.3840.3984.4048.4076.4088.4093.4095.4096
Columns: A000045, A000073, A000078, A001591, A001592 etc. (End)

Maple

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

Mathematica

Table[8(2^n-1), {n, 60}] (* Vladimir Joseph Stephan Orlovsky, Apr 18 2011 *)
LinearRecurrence[{3, -2}, {8, 24}, 30] (* Harvey P. Dale, Jan 01 2019 *)

Prog

(PARI) a(n)=8*(2^n-1) \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [8*(2^n -1): n in [1..50]]; // G. C. Greubel, May 22 2018

Crossrefs

Sequence in context: A279018 A011925 A256052 * A302489 A099041 A306056

Adjacent sequences: A159738 A159739 A159740 * A159742 A159743 A159744

Keyword

nonn,easy

Author

Al Hakanson (hawkuu(AT)gmail.com), Apr 20 2009

Extensions

More terms from R. J. Mathar, Apr 22 2009

Edited by Al Hakanson (hawkuu(AT)gmail.com), May 11 2009

Comments claiming negative entries deleted by R. J. Mathar, Aug 24 2009

Status

approved