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, 4294967288, 8589934584, 17179869176, 34359738360

Offset: 1

Author

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

Keywords

• nonn
• easy

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

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

Examples

			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)
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A000079, A000225, A036563, A159742, A159743, A159744, A159746, A159747, A159748.

Cf. A000918, A028399, A161770, A173787, A175161, A175166.

Programs

Magma

[8*(2^n -1): n in [1..50]]; // G. C. Greubel, May 22 2018

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 *)

PARI

a(n)=8*(2^n-1) \\ Charles R Greathouse IV, Sep 24 2015

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)

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

From Elmo R. Oliveira, Jun 15 2025: (Start)

E.g.f.: 8*exp(x)*(exp(x) - 1).

a(n) = 8*A000225(n) = 4*A000918(n+1) = 2*A028399(n+2). (End)

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