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 41-50 of 88 results. Next

A074547 a(n) = 3^n + 4^n + 5^n.

Original entry on oeis.org

3, 12, 50, 216, 962, 4392, 20450, 96696, 462722, 2234952, 10873250, 53199576, 261449282, 1289406312, 6376734050, 31605668856, 156925904642, 780248462472, 3883804162850, 19349526496536, 96470430052802, 481245665067432
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 4^n + 5^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 4^n + 5^n, {n, 0, 21}]

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-5*x).
E.g.f.: exp(3*x) + exp(4*x) + exp(5*x). (End)
a(n) = 12*a(n-1) - 47*a(n-2) + 60*a(n-3).

A074548 a(n) = 3^n + 4^n + 6^n.

Original entry on oeis.org

3, 13, 61, 307, 1633, 9043, 51481, 298507, 1751713, 10359523, 61573801, 367168507, 2194090993, 13129397203, 78637382521, 471273075307, 2825447921473, 16943968454083, 101629063565641, 609635780178907
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 4^n + 6^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 4^n + 6^n, {n, 0, 21}]
LinearRecurrence[{13,-54,72},{3,13,61},30] (* Harvey P. Dale, Dec 21 2022 *)

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-6*x).
E.g.f.: exp(3*x) + exp(4*x) + exp(6*x). (End)
a(n) = 13*a(n-1) - 54*a(n-2) + 72*a(n-3).

A074549 a(n) = 3^n + 4^n + 7^n.

Original entry on oeis.org

3, 14, 74, 434, 2738, 18074, 122474, 842114, 5836898, 40635434, 283582874, 1981698194, 13858595858, 96957713594, 678496291274, 4748649600674, 33237268583618, 232647822996554, 1628482704807674, 11399171225541554
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 4^n + 7^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 4^n + 7^n, {n, 0, 20}]
LinearRecurrence[{14,-61,84},{3,14,74},20] (* Harvey P. Dale, Jun 11 2024 *)

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-7*x).
E.g.f.: exp(3*x) + exp(4*x) + exp(7*x). (End)
a(n) = 14*a(n-1) - 61*a(n-2) + 84*a(n-3).

A074550 a(n) = 3^n + 4^n + 8^n.

Original entry on oeis.org

3, 15, 89, 603, 4433, 34035, 266969, 2115723, 16849313, 134499555, 1074849449, 8594306043, 68736785393, 549824517075, 4398319729529, 35185460179563, 281479314724673, 2251817122694595, 18014467616379209, 144115464116024283
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 4^n + 8^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 4^n + 8^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-8*x).
E.g.f.: exp(3*x) + exp(4*x) + exp(8*x). (End)
a(n) = 15*a(n-1) - 68*a(n-2) + 96*a(n-3).

A074551 a(n) = 3^n + 4^n + 9^n.

Original entry on oeis.org

3, 16, 106, 820, 6898, 60316, 536266, 4801540, 43118818, 387702316, 3487892026, 31385431060, 282446845138, 2541934531516, 22877065673386, 205892220185380, 1853024526865858, 16677199008675916, 150094704403896346
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 4^n + 9^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 4^n + 9^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-4*x) + 1/(1-9*x).
E.g.f.: exp(3*x) + exp(4*x) + exp(9*x). (End)
a(n) = 16*a(n-1) - 75*a(n-2) + 108*a(n-3).

A074552 a(n) = 3^n + 5^n + 7^n.

Original entry on oeis.org

3, 15, 83, 495, 3107, 20175, 134003, 903855, 6161987, 42326415, 292299923, 2026332015, 14085959267, 98111307855, 684331371443, 4778093436975, 33385561506947, 233393582580495, 1632228682596563, 11417969833962735
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 5^n + 7^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 5^n + 7^n, {n, 0, 20}]
LinearRecurrence[{15,-71,105},{3,15,83},20] (* Harvey P. Dale, Jul 16 2020 *)

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-5*x) + 1/(1-7*x).
E.g.f.: exp(3*x) + exp(5*x) + exp(7*x). (End)
a(n) = 15*a(n-1) - 71*a(n-2) + 105*a(n-3).

A074553 a(n) = 3^n + 5^n + 8^n.

Original entry on oeis.org

3, 16, 98, 664, 4802, 36136, 278498, 2177464, 17174402, 136190536, 1083566498, 8638939864, 68964148802, 550978111336, 4404154809698, 35214904015864, 281627607648002, 2252562882278536, 18018213594168098, 144134262724445464
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 5^n + 8^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 5^n + 8^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-5*x) + 1/(1-8*x).
E.g.f.: exp(3*x) + exp(5*x) + exp(8*x). (End)
a(n) = 16*a(n-1) - 79*a(n-2) + 120*a(n-3).

A074554 a(n) = 3^n + 5^n + 9^n.

Original entry on oeis.org

3, 17, 115, 881, 7267, 62417, 547795, 4863281, 43443907, 389393297, 3496609075, 31430064881, 282674208547, 2543088125777, 22882900753555, 205921664021681, 1853172819789187, 16677944768259857, 150098450381685235
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 5^n + 9^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[3^n + 5^n + 9^n, {n, 0, 20}]
LinearRecurrence[{17,-87,135},{3,17,115},30] (* Harvey P. Dale, Nov 27 2012 *)

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-5*x) + 1/(1-9*x).
E.g.f.: exp(3*x) + exp(5*x) + exp(9*x). (End)
a(n) = 17*a(n-1) - 87*a(n-2) + 135*a(n-3).

A074555 a(n) = 3^n + 6^n + 7^n.

Original entry on oeis.org

3, 16, 94, 586, 3778, 24826, 165034, 1105666, 7450978, 50450986, 343000474, 2340300946, 16018600978, 109951298746, 756592019914, 5217760843426, 36054083523778, 249557302572106, 1729973941999354, 12008256087645106
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 6^n + 7^n: n in [0..20]]; // Vincenzo Librandi, Aug 24 2011
  • Mathematica
    Table[3^n + 6^n + 7^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-6*x) + 1/(1-7*x).
E.g.f.: exp(3*x) + exp(6*x) + exp(7*x). (End)

A074556 a(n) = 3^n + 6^n + 8^n.

Original entry on oeis.org

3, 17, 109, 755, 5473, 40787, 309529, 2379275, 18463393, 144315107, 1134267049, 8952908795, 70896790513, 562818102227, 4476415458169, 35654571422315, 284296129664833, 2268726602270147, 18115958853570889, 144724548978127835
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [3^n + 6^n + 8^n: n in [0..20]]; // Vincenzo Librandi, May 20 2011
  • Mathematica
    Table[3^n + 6^n + 8^n, {n, 0, 20}]
LinearRecurrence[{17,-90,144},{3,17,109},21] (* Harvey P. Dale, May 19 2011 *)

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-6*x) + 1/(1-8*x).
E.g.f.: e^(3*x) + e^(6*x) + e^(8*x). (End)
a(n) = 17*a(n-1) - 90*a(n-2) + 144*a(n-3); a(0)=3, a(1)=17, a(2)=109. - Harvey P. Dale, May 19 2011
Previous Showing 41-50 of 88 results. Next

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

Content is available under The OEIS End-User License Agreement.