A231643 -id:A231643 - cp's OEIS frontend

A140504 a(n) = 2^n + 4.

5, 6, 8, 12, 20, 36, 68, 132, 260, 516, 1028, 2052, 4100, 8196, 16388, 32772, 65540, 131076, 262148, 524292, 1048580, 2097156, 4194308, 8388612, 16777220, 33554436, 67108868, 134217732, 268435460, 536870916, 1073741828

Offset: 0

Paul Curtz, Jun 30 2008

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Cf. A000051 (m=0), A052548 (m=2), this sequence (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), A175162 (m=16), A175163 (m=32).

[2^n +4: n in [0..30]]; // G. C. Greubel, Jul 08 2021

Table[2^n + 4, {n, 0, 30}] (* Stefan Steinerberger, Aug 04 2008 *)
LinearRecurrence[{3,-2}, {5,6}, 40] (* Harvey P. Dale, May 26 2018 *)

a(n)=2^n+4 \\ Charles R Greathouse IV, Dec 21 2011

[2^n + 4 for n in range(0,31)] # Zerinvary Lajos, May 31 2009

G.f.: (5 - 9*x)/((1 - x)*(1 - 2*x)). - Jaume Oliver Lafont, Aug 30 2009
a(n) = 2*a(n-1) - 4 with a(0) = 5. - Vincenzo Librandi, Nov 24 2009
From Reinhard Zumkeller, Feb 28 2010: (Start)
a(n) = A173786(n,2) for n > 1.
a(n+2)*A028399(n) = A175164(2*n). (End)
From G. C. Greubel, Jul 08 2021: (Start)
a(n) = m*(2^(n-2) + 1), with m = 4.
E.g.f.: exp(2*x) + 4*exp(x). (End)

More terms from Stefan Steinerberger, Aug 04 2008

A175161 a(n) = 8*(2^n + 1).

Original entry on oeis.org

16, 24, 40, 72, 136, 264, 520, 1032, 2056, 4104, 8200, 16392, 32776, 65544, 131080, 262152, 524296, 1048584, 2097160, 4194312, 8388616, 16777224, 33554440, 67108872, 134217736, 268435464, 536870920, 1073741832, 2147483656, 4294967304, 8589934600, 17179869192

Offset: 0

Reinhard Zumkeller, Feb 28 2010

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Sequences of the form m*(2^n + 1): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), this sequence (m=8), A175162 (m=16), A175163 (m=32).

Cf. A159741, A173786, A175166.

I:=[16,24]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021

8*(2^Range[0, 40] + 1) (* G. C. Greubel, Jul 08 2021 *)
LinearRecurrence[{3,-2},{16,24},40] (* Harvey P. Dale, Feb 10 2022 *)

[8*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

a(n) = A173786(n+3, 3).
a(n) = A175166(2*n)/A159741(n) for n > 0.
a(n) = 3*a(n-1) -2*a(n-2) with a(0)=16, a(1)=24. - Vincenzo Librandi, Dec 28 2010
G.f.: 8*(2 - 3*x)/((1-x)*(1-2*x)). - Chai Wah Wu, Jun 20 2020
a(n) = 8 * A000051(n). - Alois P. Heinz, Jun 20 2020
E.g.f.: 8*(exp(2*x) + exp(x)). - G. C. Greubel, Jul 08 2021

A175162 a(n) = 16*(2^n + 1).

Original entry on oeis.org

32, 48, 80, 144, 272, 528, 1040, 2064, 4112, 8208, 16400, 32784, 65552, 131088, 262160, 524304, 1048592, 2097168, 4194320, 8388624, 16777232, 33554448, 67108880, 134217744, 268435472, 536870928, 1073741840, 2147483664, 4294967312, 8589934608, 17179869200

Offset: 0

Reinhard Zumkeller, Feb 28 2010

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Sequences of the form m*(2^n + 1): A000051 (m=1), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), this sequence (m=16), A175163 (m=32).

Cf. A173786.

I:=[32,48]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021

16*(2^Range[0,30] +1) (* or *) LinearRecurrence[{3,-2},{32,48},30] (* Harvey P. Dale, Jun 08 2017 *)

[16*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

a(n) = A173786(n+4, 4).
a(n) = 3*a(n-1) - 2*a(n-2), a(0)=32, a(1)=48. - Vincenzo Librandi, Dec 28 2010
From G. C. Greubel, Jul 08 2021: (Start)
G.f.: 16*(2 - 3*x)/((1-x)*(1-2*x)).
E.g.f.: 16*(exp(2*x) + exp(x)). (End)

A175163 a(n) = 32*(2^n + 1).

Original entry on oeis.org

64, 96, 160, 288, 544, 1056, 2080, 4128, 8224, 16416, 32800, 65568, 131104, 262176, 524320, 1048608, 2097184, 4194336, 8388640, 16777248, 33554464, 67108896, 134217760, 268435488, 536870944

Offset: 0

Reinhard Zumkeller, Feb 28 2010

nonn

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-2).

Sequences of the form m*(2^n + 1): A000051 (m=0), A052548 (m=2), A140504 (m=4), A153973 (m=6), A231643 (m=5), A175161 (m=8), A175162 (m=16), this sequence (m=32).

Cf. A173786.

I:=[64,96]; [n le 2 select I[n] else 3*Self(n-1) - 2*Self(n-2): n in [1..41]]; // G. C. Greubel, Jul 08 2021

32*(2^Range[0,40] + 1) (* G. C. Greubel, Jul 08 2021 *)

[32*(2^n +1) for n in (0..40)] # G. C. Greubel, Jul 08 2021

a(n) = A173786(n+5, 5).
a(n) = 3*a(n-1) - 2*a(n-2), a(0)=64, a(1)=96. - Vincenzo Librandi, Dec 28 2010
G.f.: 32*(2 - 3*x)/((1 - x)*(1 - 2*x)). - Chai Wah Wu, Jul 24 2020
E.g.f.: 32*(exp(2*x) + exp(x)). - G. C. Greubel, Jul 08 2021

cp's OEIS Frontend

A140504 a(n) = 2^n + 4.

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A175161 a(n) = 8*(2^n + 1).

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A175162 a(n) = 16*(2^n + 1).

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A175163 a(n) = 32*(2^n + 1).

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