A242475 -id:A242475 - cp's OEIS frontend

A246139 a(n) = 2^n + 10.

11, 12, 14, 18, 26, 42, 74, 138, 266, 522, 1034, 2058, 4106, 8202, 16394, 32778, 65546, 131082, 262154, 524298, 1048586, 2097162, 4194314, 8388618, 16777226, 33554442, 67108874, 134217738, 268435466, 536870922, 1073741834, 2147483658, 4294967306

Offset: 0

Vincenzo Librandi, Aug 18 2014

First trisection of A085688. [Bruno Berselli, Aug 19 2014]

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

Cf. Sequences of the form 2^n + k: A000079 (k=0), A000051 (k=1), A052548 (k=2), A062709 (k=3), A140504 (k=4), A168614 (k=5), A153972 (k=6), A168415 (k=7), A242475 (k=8), A188165 (k=9), this sequence (k=10).

Cf. A085688.

Magma
```
[2^n+10: n in [0..40]];
```
Mathematica
```
Table[2^n + 10, {n, 0, 40}]
```

vector(50, n, 2^(n-1)+10) \\ Derek Orr, Aug 18 2014

G.f.: (11 - 21*x)/(1 - 3*x + 2*x^2).
a(n) = A000079(n) + 10.
a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.
E.g.f.: exp(2*x) + 10*exp(x). - Elmo R. Oliveira, Nov 11 2023

A267615 a(n) = 2^n + 11.

Original entry on oeis.org

12, 13, 15, 19, 27, 43, 75, 139, 267, 523, 1035, 2059, 4107, 8203, 16395, 32779, 65547, 131083, 262155, 524299, 1048587, 2097163, 4194315, 8388619, 16777227, 33554443, 67108875, 134217739, 268435467, 536870923, 1073741835, 2147483659, 4294967307, 8589934603, 17179869195, 34359738379

Offset: 0

Ilya Gutkovskiy, Jan 18 2016

Recurrence relation b(n) = 3*b(n - 1) - 2*b(n - 2) for n>1, b(0) = k, b(1) = k + 1, gives the closed form b(n) = 2^n + k - 1.

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

Cf. sequences with closed form 2^n + k - 1: A168616 (k=-4), A028399 (k=-3), A036563 (k=-2), A000918 (k=-1), A000225 (k=0), A000079 (k=1), A000051 (k=2), A052548 (k=3), A062709 (k=4), A140504 (k=5), A168614 (k=6), A153972 (k=7), A168415 (k=8), A242475 (k=9), A188165 (k=10), A246139 (k=11), this sequence (k=12).

Cf. A156940.

[2^n+11: n in [0..30]]; // Vincenzo Librandi, Jan 19 2016

Table[2^n + 11, {n, 0, 35}]
LinearRecurrence[{3, -2}, {12, 13}, 40] (* Vincenzo Librandi, Jan 19 2016 *)

a(n) = 2^n + 11; \\ Altug Alkan, Jan 18 2016

G.f.: (12 - 23*x)/(1 - 3*x + 2*x^2).
a(n) = 3*a(n - 1) - 2*a(n - 2) for n>1, a(0)=12, a(1)=13.
a(n) = A000079(n) + A010850(n).
Sum_{n>=0} 1/a(n) = 0.367971714327125...
Lim_{n->oo} a(n + 1)/a(n) = 2.
E.g.f.: exp(2*x) + 11*exp(x). - Elmo R. Oliveira, Nov 08 2023

cp's OEIS Frontend

A246139 a(n) = 2^n + 10.

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