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 51-60 of 83 results. Next

A074562 a(n) = 4^n + 5^n + 7^n.

Original entry on oeis.org

3, 16, 90, 532, 3282, 20956, 137370, 918052, 6220962, 42568876, 293289450, 2030349172, 14102205042, 98176822396, 684595023930, 4779152829892, 33389813427522, 233410633309516, 1632297014652810, 11418243549608212
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 5^n + 7^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    Table[4^n + 5^n + 7^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-5*x) + 1/(1-7*x).
E.g.f.: exp(4*x) + exp(5*x) + exp(7*x). (End)

A074563 a(n) = 4^n + 5^n + 8^n.

Original entry on oeis.org

3, 17, 105, 701, 4977, 36917, 281865, 2191661, 17233377, 136432997, 1084556025, 8642957021, 68980394577, 551043625877, 4404418462185, 35215963408781, 281631859568577, 2252579933007557, 18018281926224345, 144134536440090941
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 5^n + 8^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    Table[4^n + 5^n + 8^n, {n, 0, 20}]
  • PARI
    vector(20, n, n--; 4^n + 5^n + 8^n) \\ G. C. Greubel, Nov 09 2018

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-5*x) + 1/(1-8*x).
E.g.f.: exp(4*x) + exp(5*x) + exp(8*x). (End)

A074564 a(n) = 4^n + 5^n + 9^n.

Original entry on oeis.org

3, 18, 122, 918, 7442, 63198, 551162, 4877478, 43502882, 389635758, 3497598602, 31434082038, 282690454322, 2543153640318, 22883164406042, 205922723414598, 1853177071709762, 16677961818988878, 150098518713741482
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 5^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    Table[4^n + 5^n + 9^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-5*x) + 1/(1-9*x).
E.g.f.: exp(4*x) + exp(5*x) + exp(9*x). (End)

A074565 a(n) = 4^n + 6^n + 7^n.

Original entry on oeis.org

3, 17, 101, 623, 3953, 25607, 168401, 1119863, 7509953, 50693447, 343990001, 2344318103, 16034846753, 110016813287, 756855672401, 5218820236343, 36058335444353, 249574353301127, 1730042274055601, 12008529803290583
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 6^n + 7^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    Table[4^n + 6^n + 7^n, {n, 0, 20}]
LinearRecurrence[{17,-94,168},{3,17,101},30] (* Harvey P. Dale, Jun 22 2013 *)

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-6*x) + 1/(1-7*x).
E.g.f.: exp(4*x) + exp(6*x) + exp(7*x). (End)
a(n) = 17*a(n-1) - 94*a(n-2) + 168*a(n-3); a(0)=3, a(1)=17, a(2)=101. - Harvey P. Dale, Jun 22 2013

A074566 a(n) = 4^n + 6^n + 8^n.

Original entry on oeis.org

3, 18, 116, 792, 5648, 41568, 312896, 2393472, 18522368, 144557568, 1135256576, 8956925952, 70913036288, 562883616768, 4476679110656, 35655630815232, 284300381585408, 2268743652999168, 18116027185627136, 144724822693773312
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 6^n + 8^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    Table[4^n + 6^n + 8^n, {n, 0, 20}]
LinearRecurrence[{18,-104,192},{3,18,116},20] (* Harvey P. Dale, Oct 16 2023 *)

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-6*x) + 1/(1-8*x).
E.g.f.: exp(4*x) + exp(6*x) + exp(8*x). (End)

A074567 a(n) = 4^n + 6^n + 9^n.

Original entry on oeis.org

3, 19, 133, 1009, 8113, 67849, 582193, 5079289, 44791873, 397760329, 3548299153, 31748050969, 284623096033, 2554993631209, 22955425054513, 206362390821049, 1855845593726593, 16694125538980489, 150196263973144273
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 6^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011
  • Mathematica
    Table[4^n + 6^n + 9^n, {n, 0, 20}]
LinearRecurrence[{19,-114,216},{3,19,133},20] (* Harvey P. Dale, Jan 08 2023 *)

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-6*x) + 1/(1-9*x).
E.g.f.: exp(4*x) + exp(6*x) + exp(9*x). (End)

A074568 a(n) = 4^n + 7^n + 8^n.

Original entry on oeis.org

3, 19, 129, 919, 6753, 50599, 383889, 2937079, 22607553, 174833479, 1357265649, 10571455639, 82577541153, 646711933159, 5076538019409, 39933007340599, 314712202247553, 2484447507541639, 19642880826869169, 155514358139135959
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 7^n + 8^n: n in [0..20]]; // Vincenzo Librandi, Aug 14 2011
  • Mathematica
    Table[4^n + 7^n + 8^n, {n, 0, 20}]
LinearRecurrence[{19,-116,224},{3,19,129},20] (* Harvey P. Dale, Aug 15 2016 *)
  • PARI
    vector(20, n, n--; 4^n + 7^n + 8^n) \\ G. C. Greubel, Nov 08 2018

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-7*x) + 1/(1-8*x).
E.g.f.: exp(4*x) + exp(7*x) + exp(8*x). (End)
a(n) = 19*a(n-1) - 116*a(n-2) + 224*a(n-3). - Wesley Ivan Hurt, Apr 19 2021

A074569 a(n) = 4^n + 7^n + 9^n.

Original entry on oeis.org

3, 20, 146, 1136, 9218, 76880, 653186, 5622896, 48877058, 428036240, 3770308226, 33362580656, 296287600898, 2638821947600, 23555283963266, 210639767346416, 1886257414388738, 16909829393522960, 151723117614386306
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 7^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 14 2011
  • Mathematica
    Table[4^n + 7^n + 9^n, {n, 0, 20}]
  • PARI
    vector(20, n, n--; 4^n + 7^n + 9^n) \\ G. C. Greubel, Nov 08 2018

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-7*x) + 1/(1-9*x).
E.g.f.: exp(4*x) + exp(7*x) + exp(9*x). (End)

A074570 a(n) = 4^n + 8^n + 9^n.

Original entry on oeis.org

3, 21, 161, 1305, 10913, 92841, 797681, 6896505, 59889473, 521900361, 4561574801, 39975188505, 351165790433, 3091688751081, 27275107401521, 241076577925305, 2134499460529793, 18928998693221001, 168109102525957841
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [4^n + 8^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 14 2011
  • Mathematica
    Table[4^n + 8^n + 9^n, {n, 0, 20}]
  • PARI
    vector(20, n, n--; 4^n + 8^n + 9^n) \\ G. C. Greubel, Nov 08 2018

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-8*x) + 1/(1-9*x).
E.g.f.: exp(4*x) + exp(8*x) + exp(9*x). (End)

A074571 a(n) = 5^n + 6^n + 7^n.

Original entry on oeis.org

3, 18, 110, 684, 4322, 27708, 179930, 1181604, 7835042, 52384428, 352707050, 2388951924, 16262210162, 111170407548, 762690752570, 5248264072644, 36206628367682, 250320112885068, 1733788251844490, 12027328411711764
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [5^n + 6^n + 7^n: n in [0..20]]; // Vincenzo Librandi, May 20 2011
  • Mathematica
    Table[5^n + 6^n + 7^n, {n, 0, 20}]
LinearRecurrence[{18,-107,210},{3,18,110},30] (* Harvey P. Dale, Apr 29 2014 *)

Formula

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-5*x) + 1/(1-6*x) + 1/(1-7*x).
E.g.f.: e^(5*x) + e^(6*x) + e^(7*x). (End)
Previous Showing 51-60 of 83 results. Next

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