A034513 -id:A034513 - cp's OEIS frontend

A074537 a(n) = 2^n + 5^n + 6^n.

3, 13, 65, 349, 1937, 10933, 62345, 358189, 2070497, 12031333, 70232825, 411627229, 2420927057, 14281405333, 84467696105, 500702595469, 2973697863617, 17689599028933, 105374654196185, 628433226862909

Offset: 0

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (13,-52,60).

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

[2^n + 5^n + 6^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica
```
Table[2^n + 5^n + 6^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-5*x) + 1/(1-6*x).
E.g.f.: exp(2*x) + exp(5*x) + exp(6*x). (End)

A074538 a(n) = 2^n + 5^n + 7^n.

Original entry on oeis.org

3, 14, 78, 476, 3042, 19964, 133338, 901796, 6155682, 42307244, 292241898, 2026156916, 14085431922, 98109721724, 684326604858, 4778079120836, 33385518525762, 233393453571404, 1632228295438218, 11417968672225556, 79887633730301202, 559022701243584284

Offset: 0

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (14,-59,70).

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

[2^n + 5^n + 7^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

A074538:=n->2^n+5^n+7^n: seq(A074538(n), n=0..30); # Wesley Ivan Hurt, Oct 06 2017

Table[2^n + 5^n + 7^n, {n, 0, 20}]
LinearRecurrence[{14,-59,70},{3,14,78},20] (* Harvey P. Dale, Dec 21 2016 *)

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x)+1/(1-5*x)+1/(1-7*x).
E.g.f.: exp(2*x)+exp(5*x)+exp(7*x). (End)
a(n) = 14*a(n-1) - 59*a(n-2) + 70*a(n-3) for n > 2. - Wesley Ivan Hurt, Oct 06 2017

A074539 a(n) = 2^n + 5^n + 8^n.

Original entry on oeis.org

3, 15, 93, 645, 4737, 35925, 277833, 2175405, 17168097, 136171365, 1083508473, 8638764765, 68963621457, 550976525205, 4404150043113, 35214889699725, 281627564666817, 2252562753269445, 18018213207009753, 144134261562708285

Offset: 0

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
D. Suprijanto, I. W. Suwarno, Observation on Sums of Powers of Integers Divisible by 3k-1, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, pp. 2211-2217.
Index entries for linear recurrences with constant coefficients, signature (15,-66,80).

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

[2^n + 5^n + 8^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica
```
Table[2^n + 5^n + 8^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-5*x) + 1/(1-8*x).
E.g.f.: exp(2*x) + exp(5*x) + exp(8*x). (End)

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

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (16,-73,90).

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

[2^n + 5^n + 9^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

A074540:=n->2^n + 5^n + 9^n: seq(A074540(n), n=0..30); # Wesley Ivan Hurt, Oct 06 2017

Mathematica
```
Table[2^n + 5^n + 9^n, {n, 0, 20}]
```

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

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (15,-68,84).

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

[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}]
```

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

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (16,-76,96).

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

[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}]
```

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

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (17,-84,108).

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

[2^n + 6^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2011

Table[2^n + 6^n + 9^n, {n, 0, 20}]
LinearRecurrence[{17,-84,108},{3,17,121},30] (* Harvey P. Dale, Feb 20 2015 *)

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

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (17,-86,112).

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

[ 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}]
```

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

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (18,-95,126).

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

[ 2^n + 7^n + 9^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011

Table[2^n + 7^n + 9^n, {n, 0, 20}]
LinearRecurrence[{18,-95,126},{3,18,134},20] (* Harvey P. Dale, Apr 13 2019 *)

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

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (19,-106,144).

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

[ 2^n + 8^n + 9^n: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011

Table[2^n + 8^n + 9^n, {n, 0, 20}]
LinearRecurrence[{19,-106,144},{3,19,149},20] (* Harvey P. Dale, May 31 2013 *)

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).

cp's OEIS Frontend

A074537 a(n) = 2^n + 5^n + 6^n.

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Magma

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A074538 a(n) = 2^n + 5^n + 7^n.

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Magma

Maple

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A074539 a(n) = 2^n + 5^n + 8^n.

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Magma

Mathematica

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

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Magma

Maple

Mathematica

Formula

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

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Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs