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 29 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

A155596 a(n) = 5^n - 2^n + 1^n.

Original entry on oeis.org

1, 4, 22, 118, 610, 3094, 15562, 77998, 390370, 1952614, 9764602, 48826078, 244136530, 1220694934, 6103499242, 30517545358, 152587825090, 762939322054, 3814697003482, 19073485803838, 95367430592050, 476837156105974
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

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

Programs

Formula

G.f.: 1/(1-5*x)-1/(1-2*x)+1/(1-x).
E.g.f.: e^(5*x) - e^(2*x) + e^x.
a(n) = 7*a(n-1)-10*a(n-2)+4 with a(0)=1, a(1)=4. - Vincenzo Librandi, Jul 21 2010
a(n) = A005057(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

A155590 a(n) = 7^n + 2^n - 1.

Original entry on oeis.org

1, 8, 52, 350, 2416, 16838, 117712, 823670, 5765056, 40354118, 282476272, 1977328790, 13841291296, 96889018598, 678223089232, 4747561542710, 33232930635136, 232630514118278, 1628413598172592, 11398895185897430, 79792266298660576, 558545864085381158, 3909821048587182352
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 24 2009

Keywords

Links

Crossrefs

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590.

Programs

Formula

G.f.: 1/(1-7*x)+1/(1-2*x)-1/(1-x).
E.g.f.: exp(7*x)+exp(2*x)-exp(x).
a(n) = 9*a(n-1)-14*a(n-2)-6 with a(0) = 1, a(1) = 8. - Vincenzo Librandi, Jul 21 2010
a(n) = A074602(n)-1. - R. J. Mathar, Mar 10 2022

A155592 8^n+2^n-1^n.

Original entry on oeis.org

1, 9, 67, 519, 4111, 32799, 262207, 2097279, 16777471, 134218239, 1073742847, 8589936639, 68719480831, 549755822079, 4398046527487, 35184372121599, 281474976776191, 2251799813816319, 18014398509744127, 144115188076380159
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 24 2009

Keywords

Links

Crossrefs

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590.

Programs

  • Mathematica
    Table[8^n+2^n-1^n,{n,0,30}] (* or *) LinearRecurrence[{11,-26,16},{1,9,67},30] (* Harvey P. Dale, Jul 09 2017 *)
  • PARI
    a(n)=8^n+2^n-1 \\ Charles R Greathouse IV, Jun 11 2015

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)=9 - Vincenzo Librandi, Jul 21 2010
a(n) = A074603(n)-1. - R. J. Mathar, Mar 10 2022

A155593 a(n) = 9^n + 2^n - 1.

Original entry on oeis.org

1, 10, 84, 736, 6576, 59080, 531504, 4783096, 43046976, 387421000, 3486785424, 31381061656, 282429540576, 2541865836520, 22876792471344, 205891132127416, 1853020188917376, 16677181699797640, 150094635297261264
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 24 2009

Keywords

Links

Crossrefs

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590, A155592.

Programs

  • Mathematica
    Table[9^n+2^n-1,{n,0,30}] (* or *) LinearRecurrence[{12,-29,18},{1,10,84},30] (* Harvey P. Dale, Sep 09 2022 *)
  • PARI
    a(n)=9^n+2^n-1^n \\ Charles R Greathouse IV, Jun 11 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)=10. - Vincenzo Librandi, Jul 21 2010
a(n) = A074604(n)-1. - R. J. Mathar, Mar 10 2022

A155594 10^n+2^n-1.

Original entry on oeis.org

1, 11, 103, 1007, 10015, 100031, 1000063, 10000127, 100000255, 1000000511, 10000001023, 100000002047, 1000000004095, 10000000008191, 100000000016383, 1000000000032767, 10000000000065535, 100000000000131071
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 24 2009

Keywords

Links

Crossrefs

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590, A155592, A155593.

Programs

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)=11 - Vincenzo Librandi, Jul 21 2010
a(0)=1, a(1)=11, a(2)=103, a(n)=13*a(n-1)-32*a(n-2)+20*a(n-3). - Harvey P. Dale, Mar 07 2015
a(n) = A050621(n+1)-1. - R. J. Mathar, Mar 10 2022
Showing 1-10 of 29 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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