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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A074540 a(n) = 2^n + 5^n + 9^n.

Original entry on oeis.org

3, 16, 110, 862, 7202, 62206, 547130, 4861222, 43437602, 389374126, 3496551050, 31429889782, 282673681202, 2543086539646, 22882895986970, 205921649705542, 1853172776808002, 16677944639250766, 150098449994526890, 1350870791159844502, 12157760826489618002
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

Formula

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-5*x) + 1/(1-9*x).
E.g.f.: exp(2*x) + exp(5*x) + exp(9*x). (End)
a(n) = 16*a(n-1) - 73*a(n-2) + 90*a(n-3) for n > 2. - Wesley Ivan Hurt, Oct 06 2017

A074541 a(n) = 2^n + 6^n + 7^n.

Original entry on oeis.org

3, 15, 89, 567, 3713, 24615, 164369, 1103607, 7444673, 50431815, 342942449, 2340125847, 16018073633, 109949712615, 756587253329, 5217746527287, 36054040542593, 249557173563015, 1729973554841009, 12008254925907927
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [2^n + 6^n + 7^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011
  • Mathematica
    Table[2^n + 6^n + 7^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-6*x) + 1/(1-7*x).
E.g.f.: exp(2*x) + exp(6*x) + exp(7*x). (End)

A074542 a(n) = 2^n + 6^n + 8^n.

Original entry on oeis.org

3, 16, 104, 736, 5408, 40576, 308864, 2377216, 18457088, 144295936, 1134209024, 8952733696, 70896263168, 562816516096, 4476410691584, 35654557106176, 284296086683648, 2268726473261056, 18115958466412544, 144724547816390656
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [2^n + 6^n + 8^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2011
  • Mathematica
    Table[2^n + 6^n + 8^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-6*x) + 1/(1-8*x).
E.g.f.: exp(2*x) + exp(6*x) + exp(8*x). (End)
a(n) = 16*a(n-1) - 76*a(n-2) + 96*a(n-3). - Wesley Ivan Hurt, Jun 26 2022

A074543 a(n) = 2^n + 6^n + 9^n.

Original entry on oeis.org

3, 17, 121, 953, 7873, 66857, 578161, 5063033, 44726593, 397498697, 3547251601, 31743858713, 284606322913, 2554926530537, 22955156635441, 206361317111993, 1855841298824833, 16694108359242377, 150196195253929681
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [2^n + 6^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2011
  • Mathematica
    Table[2^n + 6^n + 9^n, {n, 0, 20}]
LinearRecurrence[{17,-84,108},{3,17,121},30] (* Harvey P. Dale, Feb 20 2015 *)

Formula

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-6*x) + 1/(1-9*x).
E.g.f.: exp(2*x) + exp(6*x) + exp(9*x). (End)
a(n) = 17*a(n-1) - 84*a(n-2) + 108*a(n-3); a(0)=3, a(1)=17, a(2)=121. - Harvey P. Dale, Feb 20 2015

A074544 a(n) = 2^n + 7^n + 8^n.

Original entry on oeis.org

3, 17, 117, 863, 6513, 49607, 379857, 2920823, 22542273, 174571847, 1356218097, 10567263383, 82560768033, 646644832487, 5076269600337, 39931933631543, 314707907345793, 2484430327803527, 19642812107654577, 155514083261753303
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [ 2^n + 7^n + 8^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[2^n + 7^n + 8^n, {n, 0, 20}]

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-7*x) + 1/(1-8*x).
E.g.f.: exp(2*x) + exp(7*x) + exp(8*x). (End)
a(n) = 17*a(n-1) - 86*a(n-2) + 112*a(n-3).

A074545 a(n) = 2^n + 7^n + 9^n.

Original entry on oeis.org

3, 18, 134, 1080, 8978, 75888, 649154, 5606640, 48811778, 427774608, 3769260674, 33358388400, 296270827778, 2638754846928, 23555015544194, 210638693637360, 1886253119486978, 16909812213784848, 151723048895171714
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [ 2^n + 7^n + 9^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[2^n + 7^n + 9^n, {n, 0, 20}]
LinearRecurrence[{18,-95,126},{3,18,134},20] (* Harvey P. Dale, Apr 13 2019 *)

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-7*x) + 1/(1-9*x).
E.g.f.: exp(2*x) + exp(7*x) + exp(9*x). (End)
a(n) = 18*a(n-1) - 95*a(n-2) + 126*a(n-3).

A074546 a(n) = 2^n + 8^n + 9^n.

Original entry on oeis.org

3, 19, 149, 1249, 10673, 91849, 793649, 6880249, 59824193, 521638729, 4560527249, 39970996249, 351149017313, 3091621650409, 27274838982449, 241075504216249, 2134495165628033, 18928981513482889, 168109033806743249
Offset: 0

Views

Author

Robert G. Wilson v, Aug 23 2002

Keywords

Links

Crossrefs

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

Programs

  • Magma
    [ 2^n + 8^n + 9^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011
  • Mathematica
    Table[2^n + 8^n + 9^n, {n, 0, 20}]
LinearRecurrence[{19,-106,144},{3,19,149},20] (* Harvey P. Dale, May 31 2013 *)

Formula

From Mohammad K. Azarian, Dec 28 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-8*x) + 1/(1-9*x).
E.g.f.: exp(2*x) + exp(8*x) + exp(9*x). (End)
a(n) = 19*a(n-1) - 106*a(n-2) + 144*a(n-3).

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).
Previous Showing 41-50 of 100 results. Next

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