A155600 -id:A155600 - cp's OEIS frontend

A155610 5^n - 3^n + 1.

1, 3, 17, 99, 545, 2883, 14897, 75939, 384065, 1933443, 9706577, 48650979, 243609185, 1219108803, 6098732657, 30503229219, 152544843905, 762810312963, 3814309845137, 19072324066659, 95363944856225, 476826697849923

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Index entries for linear recurrences with constant coefficients, signature (9,-23,15).

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

Table[5^n-3^n+1,{n,0,30}] (* or *) LinearRecurrence[{9,-23,15},{1,3,17},31] (* Harvey P. Dale, Jan 06 2012 *)

a(n)=5^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 1/(1-5*x)-1/(1-3*x)+1/(1-x).
E.g.f.: e^(5*x)-e^(3*x)+e^x.
a(n) = 8*a(n-1)-15*a(n-2)+8 with a(0)=1, a(1)=3. - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=3, a(2)=17, a(n)=9*a(n-1)-23*a(n-2)+15*a(n-3). - Harvey P. Dale, Jan 06 2012

A155606 a(n) = 8^n + 3^n - 1.

Original entry on oeis.org

1, 10, 72, 538, 4176, 33010, 262872, 2099338, 16783776, 134237410, 1073800872, 8590111738, 68720008176, 549757408210, 4398051294072, 35184386437738, 281475019757376, 2251799942825410, 18014398896902472, 144115189238117338

Offset: 0

Mohammad K. Azarian, Jan 25 2009

			G.f. = 1 + 10*x + 72*x^2 + 538*x^3 + 4176*x^4 + 33010*x^5 + 262872*x^6 + ...

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

Cf. A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603, A155604, A155605.

A155606:=n->8^n+3^n-1: seq(A155606(n), n=0..30); # Wesley Ivan Hurt, Jan 24 2017

a(n)=8^n+3^n-1 \\ Charles R Greathouse IV, Jun 11 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)=10. - Vincenzo Librandi, Jul 21 2010

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

cp's OEIS Frontend

A155610 5^n - 3^n + 1.

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A155606 a(n) = 8^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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