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.

Previous Showing 11-20 of 21 results. Next

A198689 8*7^n-1.

Original entry on oeis.org

7, 55, 391, 2743, 19207, 134455, 941191, 6588343, 46118407, 322828855, 2259801991, 15818613943, 110730297607, 775112083255, 5425784582791, 37980492079543, 265863444556807, 1861044111897655, 13027308783283591, 91191161482985143
Offset: 0

Views

Author

Vincenzo Librandi, Oct 29 2011

Keywords

Links

Crossrefs

Cf. A024075, A048473, A081655, A198480, A198647.

Programs

  • Magma
    [8*7^n-1: n in [0..30]]

Formula

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.
G.f. ( 7-x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198690 9*7^n-1.

Original entry on oeis.org

8, 62, 440, 3086, 21608, 151262, 1058840, 7411886, 51883208, 363182462, 2542277240, 17795940686, 124571584808, 872001093662, 6104007655640, 42728053589486, 299096375126408, 2093674625884862, 14655722381194040, 102590056668358286
Offset: 0

Views

Author

Vincenzo Librandi, Oct 29 2011

Keywords

Links

Crossrefs

Cf. A024075, A048473, A081655, A198480, A198647.

Programs

  • Magma
    [9*7^n-1: n in [0..30]]
  • Mathematica
    9*7^Range[0,30]-1 (* or *) LinearRecurrence[{8,-7},{8,62},30] (* Harvey P. Dale, Apr 22 2019 *)

Formula

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.
G.f. ( 8-2*x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198691 10*7^n-1.

Original entry on oeis.org

9, 69, 489, 3429, 24009, 168069, 1176489, 8235429, 57648009, 403536069, 2824752489, 19773267429, 138412872009, 968890104069, 6782230728489, 47475615099429, 332329305696009, 2326305139872069, 16284135979104489, 113988951853731429
Offset: 0

Views

Author

Vincenzo Librandi, Oct 29 2011

Keywords

Links

Crossrefs

Cf. A024075, A048473, A081655, A198480, A198647.

Programs

  • Magma
    [10*7^n-1: n in [0..30]]
  • Mathematica
    10*7^Range[0,20]-1 (* or *) LinearRecurrence[{8,-7},{9,69},20] (* Harvey P. Dale, Mar 30 2016 *)

Formula

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.
G.f. ( 9-3*x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198692 a(n) = 11*7^n-1.

Original entry on oeis.org

10, 76, 538, 3772, 26410, 184876, 1294138, 9058972, 63412810, 443889676, 3107227738, 21750594172, 152254159210, 1065779114476, 7460453801338, 52223176609372, 365562236265610, 2558935653859276, 17912549577014938
Offset: 0

Views

Author

Vincenzo Librandi, Oct 29 2011

Keywords

Links

Crossrefs

Cf. A024075, A048473, A081655, A198480, A198647.

Programs

  • Magma
    [11*7^n-1: n in [0..30]]
  • Mathematica
    11 (7^Range[0, 30]) - 1 (* Wesley Ivan Hurt, Jan 21 2017 *)

Formula

a(n) = 7*a(n-1)+6. a(n) = 8*a(n-1)-7*a(n-2), n>1.
G.f.: ( 10-4*x ) / ( (7*x-1)*(x-1) ). - R. J. Mathar, Oct 30 2011

A198763 a(n) = 4*5^n-1.

Original entry on oeis.org

3, 19, 99, 499, 2499, 12499, 62499, 312499, 1562499, 7812499, 39062499, 195312499, 976562499, 4882812499, 24414062499, 122070312499, 610351562499, 3051757812499, 15258789062499, 76293945312499, 381469726562499, 1907348632812499
Offset: 0

Views

Author

Vincenzo Librandi, Oct 30 2011

Keywords

Links

Crossrefs

Cf. A024049, A057651, A081655.

Programs

  • Magma
    [4*5^n-1: n in [0..30]]
  • Mathematica
    CoefficientList[Series[(3 + x)/(1 - 6*x + 5*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
NestList[5#+4&,3,30] (* or *) LinearRecurrence[{6,-5},{3,19},30] (* Harvey P. Dale, Jul 03 2021 *)

Formula

a(n) = 5*a(n-1)+4.
a(n) = 6*a(n-1)-5*a(n-2), n>1.
G.f.: (3 + x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 04 2013

A198765 7*5^n-1.

Original entry on oeis.org

6, 34, 174, 874, 4374, 21874, 109374, 546874, 2734374, 13671874, 68359374, 341796874, 1708984374, 8544921874, 42724609374, 213623046874, 1068115234374, 5340576171874, 26702880859374, 133514404296874
Offset: 0

Views

Author

Vincenzo Librandi, Oct 30 2011

Keywords

Links

Crossrefs

Cf. A024049, A057651, A081655.

Programs

  • Magma
    [7*5^n-1: n in [0..30]];
  • Mathematica
    CoefficientList[Series[2*(3 - x)/(1 - 6*x + 5*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
7 * 5^Range[0, 19] - 1 (* Alonso del Arte, Dec 05 2013 *)

Formula

a(n) = 5*a(n-1) + 4.
a(n) = 6*a(n-1) - 5*a(n-2), n > 1.
G.f.: 2*(3 - x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 04 2013

A198766 a(n) = (7*5^n - 1)/2.

Original entry on oeis.org

3, 17, 87, 437, 2187, 10937, 54687, 273437, 1367187, 6835937, 34179687, 170898437, 854492187, 4272460937, 21362304687, 106811523437, 534057617187, 2670288085937, 13351440429687, 66757202148437, 333786010742187, 1668930053710937
Offset: 0

Views

Author

Vincenzo Librandi, Oct 30 2011

Keywords

Links

Crossrefs

Cf. A024049, A057651, A081655.

Programs

  • Magma
    [(7*5^n-1)/2: n in [0..30]];
  • Mathematica
    CoefficientList[Series[(3 - x)/(1 - 6*x + 5*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)
LinearRecurrence[{6,-5},{3,17},30] (* Harvey P. Dale, Jan 23 2015 *)

Formula

a(n) = 5*a(n-1)+2.
a(n) = 6*a(n-1)-5*a(n-2), n>1.
G.f.: (3 - x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 04 2013
E.g.f.: exp(x)*(7*exp(4*x) - 1)/2. - Stefano Spezia, Mar 08 2025

A198767 8*5^n-1.

Original entry on oeis.org

7, 39, 199, 999, 4999, 24999, 124999, 624999, 3124999, 15624999, 78124999, 390624999, 1953124999, 9765624999, 48828124999, 244140624999, 1220703124999, 6103515624999, 30517578124999, 152587890624999, 762939453124999
Offset: 0

Views

Author

Vincenzo Librandi, Oct 30 2011

Keywords

Links

Crossrefs

Cf. A024049, A057651, A081655.

Programs

  • Magma
    [8*5^n-1: n in [0..30]];
  • Mathematica
    CoefficientList[Series[(7 - 3*x)/(1 - 6*x + 5*x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 04 2013 *)

Formula

a(n) = 5*a(n-1)+4.
a(n) = 6*a(n-1)-5*a(n-2), n>1.
G.f.: (7 - 3*x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 04 2013

A198768 a(n) = 9*5^n-1.

Original entry on oeis.org

8, 44, 224, 1124, 5624, 28124, 140624, 703124, 3515624, 17578124, 87890624, 439453124, 2197265624, 10986328124, 54931640624, 274658203124, 1373291015624, 6866455078124, 34332275390624, 171661376953124, 858306884765624
Offset: 0

Views

Author

Vincenzo Librandi, Oct 30 2011

Keywords

Links

Crossrefs

Cf. A024049, A057651, A081655.

Programs

  • Magma
    [9*5^n-1: n in [0..30]];
  • Mathematica
    9 5^Range[0, 20] - 1 (* or *) LinearRecurrence[{6, -5}, {8, 44}, 20] (* Harvey P. Dale, Nov 01 2011 *)
CoefficientList[Series[(8 - 4 x)/(1 - 6 x + 5 x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jan 03 2013 *)

Formula

a(n) = 5*a(n-1)+4.
a(n) = 6*a(n-1)-5*a(n-2), n > 1.
G.f.: (8 - 4*x)/(1 - 6*x + 5*x^2). - Vincenzo Librandi, Jan 03 2013

A198769 a(n) = (9*5^n-1)/4.

Original entry on oeis.org

2, 11, 56, 281, 1406, 7031, 35156, 175781, 878906, 4394531, 21972656, 109863281, 549316406, 2746582031, 13732910156, 68664550781, 343322753906, 1716613769531, 8583068847656, 42915344238281, 214576721191406, 1072883605957031, 5364418029785156, 26822090148925781
Offset: 0

Views

Author

Vincenzo Librandi, Oct 30 2011

Keywords

Links

Crossrefs

Cf. A024049, A057651, A081655.

Programs

  • Magma
    [(9*5^n-1)/4: n in [0..30]];
  • Mathematica
    (9*5^Range[0,30]-1)/4 (* or *) LinearRecurrence[{6,-5},{2,11},30] (* Harvey P. Dale, May 07 2012 *)

Formula

a(n) = 5*a(n-1)+1.
a(n) = 6*a(n-1)-5*a(n-2), n>1.
G.f.: (2-x)/(5*x^2-6*x+1). - Harvey P. Dale, May 07 2012
Previous Showing 11-20 of 21 results. Next

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

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