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.

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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

A155602 4^n + 3^n - 1.

Original entry on oeis.org

1, 6, 24, 90, 336, 1266, 4824, 18570, 72096, 281826, 1107624, 4371450, 17308656, 68703186, 273218424, 1088090730, 4338014016, 17309009346, 69106897224, 276040168410, 1102998412176, 4408506864306, 17623567104024, 70462887356490
Offset: 0

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

Cf. A074501, A020515, A155588, A155590, A155592-A155594, A155596-A155601.

Programs

Formula

G.f.: 1/(1-4*x)+1/(1-3*x)-1/(1-x). E.g.f.: e^(4*x)+e^(3*x)-e^x.
a(n) = 7*a(n-1) - 12*a(n-2) -6, n>1 - Gary Detlefs, Jun 21 2010
a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3), n>2, a(0)=1, a(1)=6, a(2)=24. - L. Edson Jeffery, Oct 17 2012
a(n) = A074605(n)-1. - R. J. Mathar, Mar 10 2022

A155603 a(n) = 5^n+3^n-1.

Original entry on oeis.org

1, 7, 33, 151, 705, 3367, 16353, 80311, 397185, 1972807, 9824673, 49005271, 244672065, 1222297447, 6108298593, 30531927031, 152630937345, 763068593287, 3815084686113, 19074648589591, 95370918425025, 476847618556327
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, A155601, A155602.

Programs

Formula

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)=7. - Vincenzo Librandi, Jul 21 2010
a(n) = A074606(n)-1. - R. J. Mathar, Mar 10 2022

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

Views

Author

Mohammad K. Azarian, Jan 25 2009

Keywords

Links

Crossrefs

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

Programs

Formula

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

A074527 a(n) = 2^n + 3^n + 5^n.

Original entry on oeis.org

3, 10, 38, 160, 722, 3400, 16418, 80440, 397442, 1973320, 9825698, 49007320, 244676162, 1222305640, 6108314978, 30531959800, 152631002882, 763068724360, 3815084948258, 19074649113880, 95370919473602, 476847620653480
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

Cf. A001550, A001576, A034513, A001579, A074501-A074580.

Programs

Formula

From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-3*x) + 1/(1-5*x).
E.g.f.: exp(2*x) + exp(3*x) + exp(5*x). (End)
a(n) = 10*a(n-1) - 31*a(n-2) + 30*a(n-3). - Wesley Ivan Hurt, May 26 2024
Previous Showing 11-20 of 99 results. Next

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