A155588 -id:A155588 - cp's OEIS frontend

A155589 a(n) = 6^n + 2^n - 1.

1, 7, 39, 223, 1311, 7807, 46719, 280063, 1679871, 10078207, 60467199, 362799103, 2176786431, 13060702207, 78364180479, 470185017343, 2821109972991, 16926659575807, 101559956930559, 609359740534783, 3656158441111551, 21936950642475007, 131621703846461439

Offset: 0

Mohammad K. Azarian, Jan 24 2009

Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

Cf. A074501, A074600, A005057, A005056, A099393, A155588.

Table[6^n + 2^n - 1, {n, 0, 25}] (* Paolo Xausa, Jul 30 2024 *)

a(n)=6^n+2^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-6*x)+1/(1-2*x)-1/(1-x).
E.g.f.: exp(6*x)+exp(2*x)-exp(x).
a(n) = 8*a(n-1)-12*a(n-2)-5 with a(0) = 1, a(1) = 7. - Vincenzo Librandi, Jul 21 2010

A155595 11^n+2^n-1.

Original entry on oeis.org

1, 12, 124, 1338, 14656, 161082, 1771624, 19487298, 214359136, 2357948202, 25937425624, 285311672658, 3138428380816, 34522712152122, 379749833599624, 4177248169448418, 45949729863637696, 505447028499424842

Offset: 0

Mohammad K. Azarian, Jan 24 2009

Index entries for linear recurrences with constant coefficients, signature (14,-35,22).

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590, A155592, A155593, A155594.

a(n)=11^n+2^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-11*x)+1/(1-2*x)-1/(1-x). E.g.f.: e^(11*x)+e^(2*x)-e^x.

a(n)=13*a(n-1)-22*a(n-2)-10 with a(0)=1, a(1)=12 - Vincenzo Librandi, Jul 21 2010

A155616 5^n + 4^n - 1.

Original entry on oeis.org

1, 8, 40, 188, 880, 4148, 19720, 94508, 456160, 2215268, 10814200, 53022428, 260917840, 1287811988, 6371951080, 31591319948, 156882857920, 780119322308, 3883416742360, 19348364235068, 96466943268400, 481235204714228

Offset: 0

Mohammad K. Azarian, Jan 27 2009

Index entries for linear recurrences with constant coefficients, signature (10,-29,20).

Cf. A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615.

a(n)=5^n+4^n-1 \\ Charles R Greathouse IV, Oct 16 2015

G.f.: 1/(1-5*x)+1/(1-4*x)-1/(1-x).
E.g.f.: e^(5*x)+e^(4*x)-e^x.
a(n) = 9*a(n-1)-20*a(n-2)-12 with a(0)=1, a(1)=8 - Vincenzo Librandi, Jul 21 2010

A155617 a(n) = 6^n + 4^n - 1.

Original entry on oeis.org

1, 9, 51, 279, 1551, 8799, 50751, 296319, 1745151, 10339839, 61514751, 366991359, 2193559551, 13127802879, 78632599551, 471258726399, 2825404874751, 16943839313919, 101628676145151, 609634617917439, 3657257951690751

Offset: 0

Mohammad K. Azarian, Jan 27 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-34,24).

Cf. A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616.

[6^n+4^n-1: n in [0..20]]; // Vincenzo Librandi, Feb 16 2013

I:=[1,9,51]; [n le 3 select I[n] else 11*Self(n-1)-34*Self(n-2)+24*Self(n-3): n in [1..25]]; // Vincenzo Librandi, Feb 16 2013

Table[(6^n + 4^n - 1^n), {n, 0, 30}] (* Vincenzo Librandi, Feb 16 2013 *)
LinearRecurrence[{11,-34,24},{1,9,51},30] (* Harvey P. Dale, Mar 30 2019 *)

a(n)=6^n+4^n-1 \\ Charles R Greathouse IV, Oct 16 2015

G.f.: 1/(1-6*x)+1/(1-4*x)-1/(1-x).
E.g.f.: exp(6*x) + exp(4*x) - exp(x).
a(n) = 10*a(n-1)-24*a(n-2) -15, n>1 - Gary Detlefs, Jun 21 2010
a(n) = 11*a(n-1)-34*a(n-2)+24*a(n-3). - Vincenzo Librandi, Feb 16 2013

A155618 a(n) = 7^n+4^n-1^n.

Original entry on oeis.org

1, 10, 64, 406, 2656, 17830, 121744, 839926, 5830336, 40615750, 283523824, 1981521046, 13858064416, 96956119270, 678491508304, 4748635251766, 33237225536896, 232647693856390, 1628482317387184, 11399170063280086

Offset: 0

Mohammad K. Azarian, Jan 27 2009

nonn

Index entries for linear recurrences with constant coefficients, signature (12,-39,28).

A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616, A155617

A155618:=n->7^n+4^n-1: seq(A155618(n), n=0..30); # Wesley Ivan Hurt, Apr 11 2017

Table[7^n+4^n-1,{n,0,20}] (* or *) LinearRecurrence[{12,-39,28},{1,10,64},20] (* Harvey P. Dale, Feb 04 2014 *)

G.f.: 1/(1-7*x)+1/(1-4*x)-1/(1-x). E.g.f.: e^(7*x)+e^(4*x)-e^x.
a(n) = 11*a(n-1)-28*a(n-2)-18 with a(0)=1, a(1)=10 [Vincenzo Librandi, Jul 21 2010]
a(0)=1, a(1)=10, a(2)=64, a(n) = 12*a(n-1)-39*a(n-2)+28*a(n-3). - Harvey P. Dale, Feb 04 2014

A155619 8^n+4^n-1^n.

Original entry on oeis.org

1, 11, 79, 575, 4351, 33791, 266239, 2113535, 16842751, 134479871, 1074790399, 8594128895, 68736253951, 549822922751, 4398314946559, 35185445830655, 281479271677951, 2251816993554431, 18014467228958719, 144115462953762815

Offset: 0

Mohammad K. Azarian, Jan 27 2009

nonn

Index entries for linear recurrences with constant coefficients, signature (13,-44,32).

A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616, A155617, A155618

Table[8^n+4^n-1,{n,0,30}] (* or *) LinearRecurrence[{13,-44,32},{1,11,79},30] (* Harvey P. Dale, Jun 19 2013 *)

G.f.: 1/(1-8*x)+1/(1-4*x)-1/(1-x). E.g.f.: e^(8*x)+e^(4*x)-e^x.
a(n)=12*a(n-1)-32*a(n-2)-21 with a(0)=1, a(1)=11 [From Vincenzo Librandi, Jul 21 2010]
a(0)=1, a(1)=11, a(2)=79, a(n)=13*a(n-1)-44*a(n-2)+32*a(n-3). - Harvey P. Dale, Jun 19 2013

A155620 9^n+4^n-1.

Original entry on oeis.org

1, 12, 96, 792, 6816, 60072, 535536, 4799352, 43112256, 387682632, 3487832976, 31385253912, 282446313696, 2541932937192, 22877060890416, 205892205836472, 1853024483819136, 16677198879535752, 150094704016475856

Offset: 0

Mohammad K. Azarian, Jan 27 2009

Index entries for linear recurrences with constant coefficients, signature (14,-49,36).

A155588, A155599, A155607 - A155619.

LinearRecurrence[{14,-49,36},{1,12,96},30] (* Harvey P. Dale, Feb 02 2015 *)

G.f.: 1/(1-9*x)+1/(1-4*x)-1/(1-x). E.g.f.: e^(9*x)+e^(4*x)-e^x.
a(n)=13*a(n-1)-36*a(n-2)-24 with a(0)=1, a(1)=12 [From Vincenzo Librandi, Jul 21 2010]
a(0)=1, a(1)=12, a(2)=96, a(n)=14*a(n-1)-49*a(n-2)+36*a(n-3). - Harvey P. Dale, Feb 02 2015

A155621 10^n+4^n-1^n.

Original entry on oeis.org

1, 13, 115, 1063, 10255, 101023, 1004095, 10016383, 100065535, 1000262143, 10001048575, 100004194303, 1000016777215, 10000067108863, 100000268435455, 1000001073741823, 10000004294967295, 100000017179869183

Offset: 0

Mohammad K. Azarian, Jan 27 2009

nonn

Index entries for linear recurrences with constant coefficients, signature (15,-54,40).

A155588, A155599, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614, A155615, A155616, A155617, A155618, A155619, A155620

LinearRecurrence[{15,-54,40},{1,13,115},20] (* Harvey P. Dale, Oct 24 2016 *)

G.f.: 1/(1-10*x)+1/(1-4*x)-1/(1-x). E.g.f.: e^(10*x)+e^(4*x)-e^x.

a(n)=14*a(n-1)-40*a(n-2)-27 with a(0)=1, a(1)=13 [From Vincenzo Librandi, Jul 21 2010]

A155802 Numbers k such that (5^k + 2^k - 1)/12 is prime.

Original entry on oeis.org

3, 5, 7, 15, 65, 105, 135, 155, 235, 249, 1407, 1745, 30207, 40407, 68115

Offset: 1

Zak Seidov, Jan 27 2009

			Corresponding primes are: 11, 263, 6521, 2543134241, 225875452601146757084886003255695202165296363, 2054325274013051576593043138757255806440645138498014683534338706479543763.
Other terms are too large to be presented.

Cf. A155588.

a(11)-a(15) from Michael S. Branicky, Jul 08 2025

cp's OEIS Frontend

A155589 a(n) = 6^n + 2^n - 1.

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A155595 11^n+2^n-1.

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A155616 5^n + 4^n - 1.

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A155617 a(n) = 6^n + 4^n - 1.

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Magma

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A155618 a(n) = 7^n+4^n-1^n.

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A155619 8^n+4^n-1^n.

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A155620 9^n+4^n-1.

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A155621 10^n+4^n-1^n.

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A155802 Numbers k such that (5^k + 2^k - 1)/12 is prime.

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