A155601 -id:A155601 - cp's OEIS frontend

A155629 a(n) = 8^n - 4^n + 1.

1, 5, 49, 449, 3841, 31745, 258049, 2080769, 16711681, 133955585, 1072693249, 8585740289, 68702699521, 549688705025, 4397778075649, 35183298347009, 281470681743361, 2251782633816065, 18014329790005249, 144114913197948929, 1152920405095219201, 9223367638808264705

Offset: 0

Mohammad K. Azarian, Jan 30 2009

Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (13,-44,32).

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628.

Table[8^n - 4^n + 1, {n, 0, 25}] (* Paolo Xausa, Jul 30 2024 *)

a(n)=8^n-4^n+1 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: 1/(1-8*x)-1/(1-4*x)+1/(1-x).
E.g.f.: exp(8*x)-exp(4*x)+exp(x).
a(n) = 12*a(n-1)-32*a(n-2)+21 with a(0) = 1, a(1) = 5. - Vincenzo Librandi, Jul 21 2010

A155628 a(n) = 7^n-4^n+1^n.

Original entry on oeis.org

1, 4, 34, 280, 2146, 15784, 113554, 807160, 5699266, 40091464, 281426674, 1973132440, 13824509986, 96821901544, 677954637394, 4746487768120, 33228635602306, 232613334118024, 1628344878433714, 11398620307466200

Offset: 0

Mohammad K. Azarian, Jan 30 2009

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

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627.

Table[7^n-4^n+1,{n,0,20}] (* or *) LinearRecurrence[{12,-39,28},{1,4,34},20] (* Harvey P. Dale, Jul 16 2017 *)

a(n)=7^n-4^n+1 \\ Charles R Greathouse IV, Sep 24 2015

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)=4. - Vincenzo Librandi, Jul 21 2010

A155630 a(n) = 9^n-4^n+1^n.

Original entry on oeis.org

1, 6, 66, 666, 6306, 58026, 527346, 4766586, 42981186, 387158346, 3485735826, 31376865306, 282412759266, 2541798719466, 22876524019506, 205890058352826, 1853015893884546, 16677164519797386, 150094566577522386

Offset: 0

Mohammad K. Azarian, Jan 30 2009

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

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628, A155629.

Table[9^n-4^n+1,{n,0,20}] (* or *) LinearRecurrence[{14,-49,36},{1,6,66},20] (* Harvey P. Dale, Aug 08 2019 *)

a(n)=9^n-4^n+1 \\ Charles R Greathouse IV, Sep 24 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)=6. - Vincenzo Librandi, Jul 21 2010

A155631 10^n-4^n+1^n.

Original entry on oeis.org

1, 7, 85, 937, 9745, 98977, 995905, 9983617, 99934465, 999737857, 9998951425, 99995805697, 999983222785, 9999932891137, 99999731564545, 999998926258177, 9999995705032705, 99999982820130817, 999999931280523265

Offset: 0

Mohammad K. Azarian, Jan 30 2009

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

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628, A155629, A155630.

LinearRecurrence[{15,-54,40},{1,7,85},30] (* Harvey P. Dale, Aug 30 2017 *)

a(n)=10^n-4^n+1 \\ Charles R Greathouse IV, Sep 24 2015

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)=7 - Vincenzo Librandi, Jul 21 2010

A155632 a(n) = 11^n - 4^n + 1^n.

Original entry on oeis.org

1, 8, 106, 1268, 14386, 160028, 1767466, 19470788, 214293346, 2357685548, 25936376026, 285307476308, 3138411599506, 34522645035068, 379749565147786, 4177247095673828, 45949725568604866, 505447011319424588, 5559917244772754746, 61159090173536639348, 672749993833048381426

Offset: 0

Mohammad K. Azarian, Jan 30 2009

Paolo Xausa, Table of n, a(n) for n = 0..950
Index entries for linear recurrences with constant coefficients, signature (16,-59,44).

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631.

Table[11^n - 4^n + 1, {n, 0, 25}] (* Paolo Xausa, Jul 26 2024 *)

a(n)=11^n-4^n+1 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: 1/(1-11*x)-1/(1-4*x)+1/(1-x).
E.g.f.: e^(11*x)-e^(4*x)+e^x.
a(n) = 15*a(n-1)-44*a(n-2)+30 with a(0) = 1, a(1) = 8. - Vincenzo Librandi, Jul 21 2010

A155633 6^n+5^n-1.

Original entry on oeis.org

1, 10, 60, 340, 1920, 10900, 62280, 358060, 2070240, 12030820, 70231800, 411625180, 2420922960, 14281397140, 84467679720, 500702562700, 2973697798080, 17689598897860, 105374653934040, 628433226338620

Offset: 0

Mohammad K. Azarian, Jan 30 2009

Index entries for linear recurrences with constant coefficients, signature (12,-41,30).

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631.

a(n)=6^n+5^n-1^n \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-6*x)+1/(1-5*x)-1/(1-x). E.g.f.: e^(6*x)+e^(5*x)-e^x.

a(n)=11*a(n-1)-30*a(n-2)-20 with a(0)=1, a(1)=10 - Vincenzo Librandi, Jul 21 2010

A155624 11^n-3^n+1.

Original entry on oeis.org

1, 9, 113, 1305, 14561, 160809, 1770833, 19484985, 214352321, 2357928009, 25937365553, 285311493465, 3138427845281, 34522710549609, 379749828800273, 4177248155066745, 45949729820525441, 505447028370153609

Offset: 0

Mohammad K. Azarian, Jan 29 2009

Index entries for linear recurrences with constant coefficients, signature (15,-47,33).

Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623.

LinearRecurrence[{15,-47,33},{1,9,113},20] (* Harvey P. Dale, Nov 02 2021 *)

a(n)=11^n-3^n+1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-11*x)-1/(1-3*x)+1/(1-x). E.g.f.: e^(11*x)-e^(3*x)+e^x.

a(n)=14*a(n-1)-33*a(n-2)+20 with a(0)=1, a(1)=9 - Vincenzo Librandi, Jul 21 2010

A155625 a(n) = 11^n + 4^n - 1.

Original entry on oeis.org

1, 14, 136, 1394, 14896, 162074, 1775656, 19503554, 214424416, 2358209834, 25938473176, 285315864914, 3138445153936, 34522779252794, 379750102018696, 4177249243157474, 45949734158539456, 505447045679162954, 5559917382211708216, 61159090723292453234, 672749996032071636976

Offset: 0

Mohammad K. Azarian, Jan 29 2009

Paolo Xausa, Table of n, a(n) for n = 0..950
Index entries for linear recurrences with constant coefficients, signature (16,-59,44).

Cf. A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624.

Table[11^n + 4^n - 1, {n, 0, 25}] (* Paolo Xausa, Jul 30 2024 *)

a(n)=11^n+4^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-11*x)+1/(1-4*x)-1/(1-x).
E.g.f.: exp(11*x)+exp(4*x)-exp(x).
a(n) = 15*a(n-1)-44*a(n-2)-30 with a(0) = 1, a(1) = 14. - Vincenzo Librandi, Jul 21 2010

A155635 8^n+5^n-1.

Original entry on oeis.org

1, 12, 88, 636, 4720, 35892, 277768, 2175276, 17167840, 136170852, 1083507448, 8638762716, 68963617360, 550976517012, 4404150026728, 35214889666956, 281627564601280, 2252562753138372, 18018213206747608, 144134261562183996

Offset: 0

Mohammad K. Azarian, Jan 30 2009

Index entries for linear recurrences with constant coefficients, signature (14,-53,40).

Cf. A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631, A155632, A155633, A155634.

Table[8^n+5^n-1,{n,0,40}] (* or *) LinearRecurrence[{14,-53,40},{1,12,88},40] (* Harvey P. Dale, Jan 17 2017 *)

a(n)=8^n+5^n-1^n \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-8*x)+1/(1-5*x)-1/(1-x). E.g.f.: e^(8*x)+e^(5*x)-e^x.

a(n)=13*a(n-1)-40*a(n-2)-28 with a(0)=1, a(1)=12 - Vincenzo Librandi, Jul 21 2010

A155626 a(n) = 5^n-4^n+1.

Original entry on oeis.org

1, 2, 10, 62, 370, 2102, 11530, 61742, 325090, 1690982, 8717050, 44633822, 227363410, 1153594262, 5835080170, 29443836302, 148292923330, 745759583942, 3745977788890, 18798608421182, 94267920012850, 472439111692022

Offset: 0

Mohammad K. Azarian, Jan 29 2009

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

Cf. A054401, which is essentially a(n) - 2. Also A155588, A155589, A155590, A155592, A155593, A155594, A155595, A155596, A155597, A155598, A155599, A155600, A155601, A155622, A155623, A155624, A155625.

Table[5^n-4^n+1,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011*)
LinearRecurrence[{10,-29,20},{1,2,10},30] (* Harvey P. Dale, Oct 11 2023 *)

a(n)=5^n-4^n+1 \\ Charles R Greathouse IV, Jun 11 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)=2. - Vincenzo Librandi, Jul 21 2010
a(n) = 10*a(n-1)-29*a(n-2)+20*a(n-3). - Wesley Ivan Hurt, Jun 07 2021

cp's OEIS Frontend

A155629 a(n) = 8^n - 4^n + 1.

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A155628 a(n) = 7^n-4^n+1^n.

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A155630 a(n) = 9^n-4^n+1^n.

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A155631 10^n-4^n+1^n.

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A155632 a(n) = 11^n - 4^n + 1^n.

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A155633 6^n+5^n-1.

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A155624 11^n-3^n+1.

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A155625 a(n) = 11^n + 4^n - 1.

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