A155626 -id:A155626 - 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

A155638 a(n) = 11^n+5^n-1^n.

Original entry on oeis.org

1, 15, 145, 1455, 15265, 164175, 1787185, 19565295, 214749505, 2359900815, 25947190225, 285360498735, 3138672517345, 34523932847055, 379755937098865, 4177278686993775, 45949882451462785, 505447791438746895

Offset: 0

Mohammad K. Azarian, Jan 30 2009

Index entries for linear recurrences with constant coefficients, signature (17,-71,55).

Cf. A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637.

A155638:=n->11^n + 5^n - 1; seq(A155638(n), n=0..30); # Wesley Ivan Hurt, Jan 28 2014

Table[11^n + 5^n - 1, {n, 0, 30}] (* Wesley Ivan Hurt, Jan 28 2014 *)
LinearRecurrence[{17,-71,55},{1,15,145},30] (* Harvey P. Dale, Jul 03 2019 *)

a(n)=11^n+5^n-1 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: 1/(1-11*x)+1/(1-5*x)-1/(1-x). E.g.f.: e^(11*x)+e^(5*x)-e^x.

a(n) = 16*a(n-1)-55*a(n-2)-40 with a(0)=1, a(1)=15 - 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

A155639 a(n) = 6^n-5^n+1^n.

Original entry on oeis.org

1, 2, 12, 92, 672, 4652, 31032, 201812, 1288992, 8124572, 50700552, 313968932, 1932641712, 11839990892, 72260648472, 439667406452, 2668522016832, 16163719991612, 97745259402792, 590286253682372, 3560791008422352

Offset: 0

Mohammad K. Azarian, Jan 30 2009

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

Cf. A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638.

[6^n - 5^n + 1 : n in [0..20]]; // Wesley Ivan Hurt, Nov 20 2014

A155639:=n->6^n - 5^n + 1: seq(A155639(n), n=0..20); # Wesley Ivan Hurt, Nov 20 2014

Table[6^n - 5^n + 1, {n, 0, 20}] (* Wesley Ivan Hurt, Nov 20 2014 *)
LinearRecurrence[{12,-41,30},{1,2,12},30] (* Harvey P. Dale, Aug 23 2016 *)

a(n)=6^n-5^n+1 \\ Charles R Greathouse IV, Sep 24 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)=2. - Vincenzo Librandi, Jul 21 2010

A155640 a(n) = 7^n - 5^n + 1^n.

Original entry on oeis.org

1, 3, 25, 219, 1777, 13683, 102025, 745419, 5374177, 38400483, 272709625, 1928498619, 13597146577, 95668307283, 672119557225, 4717043931819, 33080342678977, 231867574534083, 1624598900644825, 11379821699045019, 79696898865971377, 558069026925080883

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,-47,35).

Cf. A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639.

Table[7^n - 5^n + 1, {n, 0, 25}] (* Paolo Xausa, Jul 26 2024 *)

a(n)=7^n-5^n+1 \\ Charles R Greathouse IV, Sep 24 2015

G.f.: 1/(1-7*x)-1/(1-5*x)+1/(1-x).
E.g.f.: e^(7*x)-e^(5*x)+e^x.
a(n) = 12*a(n-1)-35*a(n-2)+24 with a(0)=1, a(1)=3. - 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

A155641 8^n-5^n+1^n.

Original entry on oeis.org

1, 4, 40, 388, 3472, 29644, 246520, 2019028, 16386592, 132264604, 1063976200, 8541106468, 68475336112, 548535110764, 4391942995480, 35153854510708, 281322388820032, 2251036874232124, 18010583812216360, 144096114589527748

Offset: 0

Mohammad K. Azarian, Jan 30 2009

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

Cf. A155624, A155625, A155626, A155627, A155628, A155629, A155630, A155631, A155632, A155633, A155634, A155635, A155636, A155637, A155638, A155639, A155640.

Table[8^n-5^n+1^n,{n,0,20}] (* or *) LinearRecurrence[{14,-53,40},{1,4,40},20] (* Harvey P. Dale, May 08 2018 *)

a(n)=8^n-5^n+1 \\ 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)=4 - 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

cp's OEIS Frontend

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

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A155638 a(n) = 11^n+5^n-1^n.

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

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A155639 a(n) = 6^n-5^n+1^n.

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A155640 a(n) = 7^n - 5^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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