cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-10 of 30 results. Next

A155599 a(n) = 8^n - 2^n + 1^n.

Original entry on oeis.org

1, 7, 61, 505, 4081, 32737, 262081, 2097025, 16776961, 134217217, 1073740801, 8589932545, 68719472641, 549755805697, 4398046494721, 35184372056065, 281474976645121, 2251799813554177, 18014398509219841, 144115188075331585
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598.

Programs

Formula

G.f.: 1/(1-8*x) - 1/(1-2*x) + 1/(1-x).
E.g.f.: e^(8*x) - e^(2*x) + e^x.
a(n) = 10*a(n-1) - 16*a(n-2) + 7 with a(0)=1, a(1)=7 - Vincenzo Librandi, Jul 21 2010
a(n) = A248217(n)+1. - R. J. Mathar, Mar 10 2022

A155597 a(n) = 6^n - 2^n + 1.

Original entry on oeis.org

1, 5, 33, 209, 1281, 7745, 46593, 279809, 1679361, 10077185, 60465153, 362795009, 2176778241, 13060685825, 78364147713, 470184951809, 2821109841921, 16926659313665, 101559956406273, 609359739486209, 3656158439014401, 21936950638280705, 131621703838072833
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596.

Programs

  • Mathematica
    Table[6^n-2^n+1,{n,0,20}] (* or *) LinearRecurrence[{9,-20,12},{1,5,33},20] (* Harvey P. Dale, Jul 13 2011 *)
  • PARI
    a(n) = 6^n-2^n+1 \\ Charles R Greathouse IV, Jul 25 2011

Formula

G.f.: 1/(1-6*x)-1/(1-2*x)+1/(1-x).
E.g.f.: exp(6*x)-exp(2*x)+exp(x).
a(n) = 8*a(n-1)-12*a(n-2)+5 with a(0)=1, a(1)=5. - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=5, a(2)=33, a(n) = 9*a(n-1)-20*a(n-2)+12*a(n-3). - Harvey P. Dale, Jul 13 2011
a(n) = A248216(n)+1. - R. J. Mathar, Mar 10 2022

A155600 a(n) = 9^n-2^n+1^n.

Original entry on oeis.org

1, 8, 78, 722, 6546, 59018, 531378, 4782842, 43046466, 387419978, 3486783378, 31381057562, 282429532386, 2541865820138, 22876792438578, 205891132061882, 1853020188786306, 16677181699535498, 150094635296736978
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597, A155598, A155599.

Programs

  • Mathematica
    Table[9^n - 2^n + 1, {n, 0, 25}] (* or *)
LinearRecurrence[{12, -29, 18}, {1, 8, 78}, 26] (* Paolo Xausa, Jul 19 2024 *)
  • PARI
    a(n)=9^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-9*x)-1/(1-2*x)+1/(1-x). E.g.f.: e^(9*x)-e^(2*x)+e^x.
a(n) = 11*a(n-1)-18*a(n-2)+8 with a(0)=1, a(1)=8 - Vincenzo Librandi, Jul 21 2010
a(n) = A191465(n)+1. - R. J. Mathar, Mar 10 2022

A155598 a(n) = 7^n-2^n+1.

Original entry on oeis.org

1, 6, 46, 336, 2386, 16776, 117586, 823416, 5764546, 40353096, 282474226, 1977324696, 13841283106, 96889002216, 678223056466, 4747561477176, 33232930504066, 232630513856136, 1628413597648306, 11398895184848856
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592, A155593, A155594, A155596, A155597.

Programs

Formula

G.f.: 1/(1-7*x)-1/(1-2*x)+1/(1-x). E.g.f.: e^(7*x)-e^(2*x)+e^x.
a(n) = 9*a(n-1)-14*a(n-2)+6 with a(0)=1, a(1)=6 - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=6, a(2)=46, a(n) = 10*a(n-1)-23*a(n-2)+14*a(n-3). - Harvey P. Dale, Feb 28 2013
a(n) = A190540(n)+1. - R. J. Mathar, Mar 10 2022

A155601 a(n) = 10^n - 2^n + 1^n.

Original entry on oeis.org

1, 9, 97, 993, 9985, 99969, 999937, 9999873, 99999745, 999999489, 9999998977, 99999997953, 999999995905, 9999999991809, 99999999983617, 999999999967233, 9999999999934465, 99999999999868929, 999999999999737857, 9999999999999475713, 99999999999998951425
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    Table[10^n-2^n+1,{n,0,20}] (* or *) LinearRecurrence[{13,-32,20},{1,9,97},20] (* Harvey P. Dale, Jan 13 2022 *)
  • PARI
    a(n)=10^n-2^n+1 \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f.: 1/(1-10*x)-1/(1-2*x)+1/(1-x).
E.g.f.: e^(10*x)-e^(2*x)+e^x.
a(n) = 12*a(n-1)-20*a(n-2)+9 with a(0)=1, a(1)=9. - Vincenzo Librandi, Jul 21 2010
a(n) = A060458(n)+1. - R. J. Mathar, Mar 10 2022

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

Original entry on oeis.org

1, 5, 49, 449, 3841, 31745, 258049, 2080769, 16711681, 133955585, 1072693249, 8585740289, 68702699521, 549688705025, 4397778075649, 35183298347009, 281470681743361, 2251782633816065, 18014329790005249, 144114913197948929, 1152920405095219201, 9223367638808264705
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

Links

Crossrefs

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

Programs

Formula

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

Views

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

Links

Crossrefs

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

Programs

Formula

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

Views

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

Links

Crossrefs

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

Programs

Formula

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

Views

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

Links

Crossrefs

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

Programs

Formula

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

Views

Author

Mohammad K. Azarian, Jan 30 2009

Keywords

Links

Crossrefs

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

Programs

Formula

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
Showing 1-10 of 30 results. Next

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