A001550 -id:A001550 - cp's OEIS frontend

A074529 a(n) = 2^n + 3^n + 7^n.

3, 12, 62, 378, 2498, 17082, 118442, 825858, 5771618, 40373802, 282535322, 1977505938, 13841822738, 96890612922, 678227872202, 4747575891618, 33232973681858, 232630643258442, 1628413985593082, 11398896348158898

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 (12,-41,42).

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

[2^n + 3^n + 7^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Table[2^n + 3^n + 7^n, {n, 0, 20}]
LinearRecurrence[{12,-41,42},{3,12,62},20] (* Harvey P. Dale, Mar 29 2020 *)

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-3*x) + 1/(1-7*x).
E.g.f.: exp(2*x) + exp(3*x) + exp(7*x). (End)

A074530 a(n) = 2^n + 3^n + 8^n.

Original entry on oeis.org

3, 13, 77, 547, 4193, 33043, 262937, 2099467, 16784033, 134237923, 1073801897, 8590113787, 68720012273, 549757416403, 4398051310457, 35184386470507, 281475019822913, 2251799942956483, 18014398897164617, 144115189238641627

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,-46,48).

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

[2^n + 3^n + 8^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Table[2^n + 3^n + 8^n, {n, 0, 20}]
LinearRecurrence[{13,-46,48},{3,13,77},20] (* Harvey P. Dale, Aug 04 2025 *)

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-3*x) + 1/(1-8*x).
E.g.f.: exp(2*x) + exp(3*x) + exp(8*x). (End)

A074531 a(n) = 2^n + 3^n + 9^n.

Original entry on oeis.org

3, 14, 94, 764, 6658, 59324, 532234, 4785284, 43053538, 387440684, 3486844474, 31381238804, 282430072018, 2541867430844, 22876797254314, 205891146476324, 1853020231964098, 16677181828937804, 150094635684681754

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,-51,54).

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

[2^n + 3^n + 9^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Table[2^n + 3^n + 9^n, {n, 0, 20}]
LinearRecurrence[{14,-51,54},{3,14,94},20] (* Harvey P. Dale, Nov 29 2019 *)

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-3*x) + 1/(1-9*x).
E.g.f.: exp(2*x) + exp(3*x) + exp(9*x). (End)

A074532 a(n) = 2^n + 4^n + 5^n.

Original entry on oeis.org

3, 11, 45, 197, 897, 4181, 19785, 94637, 456417, 2215781, 10815225, 53024477, 260921937, 1287820181, 6371967465, 31591352717, 156882923457, 780119453381, 3883417004505, 19348364759357, 96466944316977, 481235206811381

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 (11,-38,40).

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

[2^n + 4^n + 5^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica
```
Table[2^n + 4^n + 5^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-4*x) + 1/(1-5*x).
E.g.f.: exp(2*x) + exp(4*x) + exp(5*x). (End)

A074533 a(n) = 2^n + 4^n + 6^n.

Original entry on oeis.org

3, 12, 56, 288, 1568, 8832, 50816, 296448, 1745408, 10340352, 61515776, 366993408, 2193563648, 13127811072, 78632615936, 471258759168, 2825404940288, 16943839444992, 101628676407296, 609634618441728

Offset: 0

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..200
T. A. Gulliver, Sums of Powers of Integers Divisible by Three, Int. J. Contemp. Math. Sciences, Vol. 7, 2012, no. 38, pp. 1895-1901. - From _N. J. A. Sloane_, Dec 22 2012
D. Suprijanto and Rusliansyah, Observation on Sums of Powers of Integers Divisible by Four, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, 2219-2226.
Index entries for linear recurrences with constant coefficients, signature (12,-44,48).

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

[2^n + 4^n + 6^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica
```
Table[2^n + 4^n + 6^n, {n, 0, 20}]
```

G.f.: 1/(1-2*x)+1/(1-4*x)+1/(1-6*x). E.g.f.: exp(2*x)+exp(4*x)+exp(6*x). - Mohammad K. Azarian, Dec 27 2008

A074534 a(n) = 2^n + 4^n + 7^n.

Original entry on oeis.org

3, 13, 69, 415, 2673, 17863, 121809, 840055, 5830593, 40616263, 283524849, 1981523095, 13858068513, 96956127463, 678491524689, 4748635284535, 33237225602433, 232647693987463, 1628482317649329, 11399170063804375

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,-50,56).

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

[2^n + 4^n + 7^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica
```
Table[2^n + 4^n + 7^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-4*x) + 1/(1-7*x).
E.g.f.: exp(2*x) + exp(4*x) + exp(7*x). (End)

A074536 a(n) = 2^n + 4^n + 9^n.

Original entry on oeis.org

3, 15, 101, 801, 6833, 60105, 535601, 4799481, 43112513, 387683145, 3487834001, 31385255961, 282446317793, 2541932945385, 22877060906801, 205892205869241, 1853024483884673, 16677198879666825, 150094704016738001

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,-62,72).

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

[2^n + 4^n + 9^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica
```
Table[2^n + 4^n + 9^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 27 2008: (Start)
G.f.: 1/(1-2*x) + 1/(1-4*x) + 1/(1-9*x).
E.g.f.: exp(2*x) + exp(4*x) + exp(9*x). (End)

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

Original entry on oeis.org

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)

cp's OEIS Frontend

A074529 a(n) = 2^n + 3^n + 7^n.

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A074530 a(n) = 2^n + 3^n + 8^n.

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Magma

Mathematica

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A074531 a(n) = 2^n + 3^n + 9^n.

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Magma

Mathematica

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A074532 a(n) = 2^n + 4^n + 5^n.

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Magma

Mathematica

Formula

A074533 a(n) = 2^n + 4^n + 6^n.

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Magma

Mathematica

Formula

A074534 a(n) = 2^n + 4^n + 7^n.

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Magma

Mathematica

Formula

A074536 a(n) = 2^n + 4^n + 9^n.

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Magma

Mathematica

Formula

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

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Magma

Mathematica