A155596 -id:A155596 - cp's OEIS frontend

A155608 10^n + 3^n - 1.

1, 12, 108, 1026, 10080, 100242, 1000728, 10002186, 100006560, 1000019682, 10000059048, 100000177146, 1000000531440, 10000001594322, 100000004782968, 1000000014348906, 10000000043046720, 100000000129140162

Offset: 0

Mohammad K. Azarian, Jan 25 2009

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

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

A155608:=n->10^n + 3^n - 1; seq(A155608(n), n=0..30); # Wesley Ivan Hurt, Apr 02 2014

Table[10^n + 3^n - 1, {n, 0, 30}] (* Wesley Ivan Hurt, Apr 02 2014 *)

a(n)=10^n+3^n-1 \\ Charles R Greathouse IV, Sep 28 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)=12. - Vincenzo Librandi, Jul 21 2010

A155622 a(n) = 11^n - 2^n + 1.

Original entry on oeis.org

1, 10, 118, 1324, 14626, 161020, 1771498, 19487044, 214358626, 2357947180, 25937423578, 285311668564, 3138428372626, 34522712135740, 379749833566858, 4177248169382884, 45949729863506626, 505447028499162700

Offset: 0

Mohammad K. Azarian, Jan 29 2009

In general: r^n - s^n + 1 = (r+s)*a(n-1)-(r*s)*a(n-2)+(r-1)*(s-1). - Vincenzo Librandi, Jul 21 2010

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

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

Table[11^n - 2^n + 1, {n, 0, 20}] (* or *) LinearRecurrence[{14, -35, 22}, {1, 10, 118}, 20] (* Harvey P. Dale, Oct 21 2013 *)

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.: exp(11*x) - exp(2*x) + exp(x).
a(n) = 13*a(n-1) - 22*a(n-2) + 10 for n>1, a(0)=1, a(1)=10. - Vincenzo Librandi, Jul 21 2010

A155604 a(n) = 6^n + 3^n - 1.

Original entry on oeis.org

1, 8, 44, 242, 1376, 8018, 47384, 282122, 1686176, 10097378, 60525224, 362974202, 2177313776, 13062288338, 78368947064, 470199333482, 2821152954176, 16926788584898, 101560344088904, 609360902271962, 3656161926847376

Offset: 0

Mohammad K. Azarian, Jan 25 2009

Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (10,-27,18).

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599, A155600, A155601, A155602, A155603.

Table[6^n + 3^n - 1, {n, 0, 25}] (* Paolo Xausa, Aug 21 2024 *)

a(n)=6^n+3^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-6*x)+1/(1-3*x)-1/(1-x).
E.g.f.: exp(6*x)+exp(3*x)-exp(x).
a(n) = 9*a(n-1)-18*a(n-2)-10 with a(0) = 1, a(1) = 8. - Vincenzo Librandi, Jul 21 2010

A155609 a(n) = 4^n - 3^n + 1.

Original entry on oeis.org

1, 2, 8, 38, 176, 782, 3368, 14198, 58976, 242462, 989528, 4017158, 16245776, 65514542, 263652488, 1059392918, 4251920576, 17050729022, 68332056248, 273715645478, 1096024843376, 4387586157902, 17560804984808, 70274600998838

Offset: 0

Mohammad K. Azarian, Jan 26 2009

Let P(A) be the power set of an n-element set A and R be a relation on P(A) such that for all x, y of P(A), xRy if x and y are intersecting. Then a(n) = |R|. - Ross La Haye, Mar 19 2009

Ross La Haye, Binary Relations on the Power Set of an n-Element Set, Journal of Integer Sequences, Vol. 12 (2009), Article 09.2.6.
Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

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

Table[4^n-3^n+1,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Feb 15 2011 *)
LinearRecurrence[{8,-19,12},{1,2,8},30] (* Harvey P. Dale, Sep 30 2018 *)

a(n)=4^n-3^n+1 \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 1/(1-4*x) - 1/(1-3*x) + 1/(1-x).
E.g.f.: exp(4*x) - exp(3*x) + exp(x).
a(n) = 7*a(n-1)-12*a(n-2)+6 with a(0)=1, a(1)=2. - Vincenzo Librandi, Jul 21 2010

A155605 7^n+3^n-1.

Original entry on oeis.org

1, 9, 57, 369, 2481, 17049, 118377, 825729, 5771361, 40373289, 282534297, 1977503889, 13841818641, 96890604729, 678227855817, 4747575858849, 33232973616321, 232630643127369, 1628413985330937, 11398896347634609

Offset: 0

Mohammad K. Azarian, Jan 25 2009

Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

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

Table[7^n+3^n-1,{n,0,20}] (* or *) LinearRecurrence[{11,-31,21},{1,9,57},20] (* Harvey P. Dale, Nov 09 2012 *)

a(n)=7^n+3^n-1 \\ Charles R Greathouse IV, Jun 11 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)=9 - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=9, a(2)=57, a(n)=11*a(n-1)-31*a(n-2)+21*a(n-3). - Harvey P. Dale, Nov 09 2012

A155610 5^n - 3^n + 1.

Original entry on oeis.org

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

A155611 6^n - 3^n + 1.

Original entry on oeis.org

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

cp's OEIS Frontend

A155608 10^n + 3^n - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A155622 a(n) = 11^n - 2^n + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A155604 a(n) = 6^n + 3^n - 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A155609 a(n) = 4^n - 3^n + 1.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A155605 7^n+3^n-1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A155610 5^n - 3^n + 1.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Maple

PARI

Formula

A155611 6^n - 3^n + 1.

Views

Author

Keywords

Links