A155610 -id:A155610 - cp's OEIS frontend

A155611 6^n - 3^n + 1.

1, 4, 28, 190, 1216, 7534, 45928, 277750, 1673056, 10058014, 60407128, 362619910, 2176250896, 13059099694, 78359381128, 470170635670, 2821066860736, 16926530304574, 101559569247928, 609358577749030, 3656154953278576

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Index entries for linear recurrences with constant coefficients, signature (10,-27,18).

Cf. A155596-A155610.

a(n)=6^n-3^n+1 \\ Charles R Greathouse IV, Jan 09 2012

G.f.: 1/(1-6*x)-1/(1-3*x)+1/(1-x). E.g.f.: e^(6*x)-e^(3*x)+e^x.
a(n)=9*a(n-1)-18*a(n-2)+10 with a(0)=1, a(1)=4 [From Vincenzo Librandi, Jul 21 2010]
E.g.f.: exp(6*x)-exp(3*x)+exp(x)= G(0) ; G(k)= 1 - 1/( 2^k + 2^k/( 3^k - 1 - 6*x*18^k/( x*6^(k+1)+(k+1)/G(k+1)))); (continued fraction, 3-step ). - Sergei N. Gladkovskii, Jan 10 2012

A155612 7^n - 3^n + 1.

Original entry on oeis.org

1, 5, 41, 317, 2321, 16565, 116921, 821357, 5758241, 40333925, 282416201, 1977149597, 13840755761, 96887416085, 678218289881, 4747547161037, 33232887522881, 232630384847045, 1628413210489961, 11398894023111677

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611.

a(n)=7^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 1/(1-7*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(7*x)-e^(3*x)+e^x.
a(n) = 10*a(n-1)-21*a(n-2)+12 with a(0)=1, a(1)=5. - Vincenzo Librandi, Jul 21 2010

A155613 8^n - 3^n + 1.

Original entry on oeis.org

1, 6, 56, 486, 4016, 32526, 261416, 2094966, 16770656, 134198046, 1073682776, 8589757446, 68718945296, 549754219566, 4398041728136, 35184357739926, 281474933663936, 2251799684545086, 18014398122061496, 144115186913594406

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Index entries for linear recurrences with constant coefficients, signature (12,-35,24).

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612.

Table[8^n-3^n+1,{n,0,20}] (* or *) LinearRecurrence[{12,-35,24},{1,6,56},20] (* Harvey P. Dale, Mar 12 2014 *)

a(n)=8^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 1/(1-8*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(8*x)-e^(3*x)+e^x.
a(n) = 11*a(n-1)-24*a(n-2)+14 with a(0)=1, a(1)=6. - Vincenzo Librandi, Jul 21 2010

A155614 9^n - 3^n + 1.

Original entry on oeis.org

1, 7, 73, 703, 6481, 58807, 530713, 4780783, 43040161, 387400807, 3486725353, 31380882463, 282429005041, 2541864234007, 22876787671993, 205891117745743, 1853020145805121, 16677181570526407, 150094634909578633

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Cf. A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612, A155613.

Table[9^n-3^n+1,{n,0,20}]  (* Harvey P. Dale, Feb 03 2011 *)

a(n)=9^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 1/(1-9*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(9*x)-e^(3*x)+e^x.
a(n) = 12*a(n-1)-27*a(n-2)+16 with a(0)=1, a(1)=7. - Vincenzo Librandi, Jul 21 2010

A155615 a(n) = 10^n - 3^n + 1.

Original entry on oeis.org

1, 8, 92, 974, 9920, 99758, 999272, 9997814, 99993440, 999980318, 9999940952, 99999822854, 999999468560, 9999998405678, 99999995217032, 999999985651094, 9999999956953280, 99999999870859838, 999999999612579512

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Index entries for linear recurrences with constant coefficients, signature (14,-43,30).

Cf. A155599, A155600, A155601, A155602, A155603, A155604, A155605, A155606, A155607, A155608, A155609, A155610, A155611, A155612, A155613, A155614.

a(n)=10^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 1/(1-10*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(3*x)+e^x.
a(n) = 13*a(n-1)-30*a(n-2)+18 with a(0)=1, a(1)=8. - 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

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]

cp's OEIS Frontend

A155611 6^n - 3^n + 1.

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A155612 7^n - 3^n + 1.

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A155613 8^n - 3^n + 1.

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A155614 9^n - 3^n + 1.

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A155615 a(n) = 10^n - 3^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.