A034513 -id:A034513 - cp's OEIS frontend

A074511 a(n) = 1^n + 4^n + 5^n.

3, 10, 42, 190, 882, 4150, 19722, 94510, 456162, 2215270, 10814202, 53022430, 260917842, 1287811990, 6371951082, 31591319950, 156882857922, 780119322310, 3883416742362, 19348364235070, 96466943268402, 481235204714230, 2401777977060042, 11991297699255790

Offset: 0

Robert G. Wilson v, Aug 23 2002

Index entries for linear recurrences with constant coefficients, signature (10,-29,20).

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

Mathematica
```
Table[1^n + 4^n + 5^n, {n, 0, 21}]
```

From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-x) + 1/(1-4*x) + 1/(1-5*x).
E.g.f.: e^x + e^(4*x) + e^(5*x). (End)
a(n) = 9*a(n-1) - 20*a(n-2) + 12 with a(0)=3, a(1)=10. - Vincenzo Librandi, Jul 21 2010

A074516 a(n) = 1^n + 5^n + 6^n.

Original entry on oeis.org

3, 12, 62, 342, 1922, 10902, 62282, 358062, 2070242, 12030822, 70231802, 411625182, 2420922962, 14281397142, 84467679722, 500702562702, 2973697798082, 17689598897862, 105374653934042, 628433226338622

Offset: 0

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-41,30).

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

[5^n+6^n+1^n: n in [0..30]]; // Vincenzo Librandi, Mar 24 2013

A074516:=n->1^n+5^n+6^n: seq(A074516(n), n=0..30); # Wesley Ivan Hurt, Jan 27 2017

Table[1^n + 5^n + 6^n, {n, 0, 20}]
LinearRecurrence[{12,-41,30},{3,12,62},20] (* Harvey P. Dale, Apr 06 2018 *)

G.f.: 1/(1-x)+1/(1-5*x)+1/(1-6*x). E.g.f.: e^x+e^(5*x)+e^(6*x). [Mohammad K. Azarian, Dec 26 2008]

a(n) = 11*a(n-1) - 30*a(n-2) + 20, n>1. [Gary Detlefs, Jun 21 2010]

A074520 1^n + 6^n + 7^n.

Original entry on oeis.org

3, 14, 86, 560, 3698, 24584, 164306, 1103480, 7444418, 50431304, 342941426, 2340123800, 16018069538, 109949704424, 756587236946, 5217746494520, 36054040477058, 249557173431944, 1729973554578866, 12008254925383640

Offset: 0

Robert G. Wilson v, Aug 23 2002

Index entries for linear recurrences with constant coefficients, signature (14,-55,42).

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

A074520:=n->1^n + 6^n + 7^n; seq(A074520(n), n=0..100); # Wesley Ivan Hurt, Nov 11 2013

Mathematica
```
Table[1 + 6^n + 7^n, {n, 0, 20}]
```

G.f.:1/(1-x)+1/(1-6*x)+1/(1-7*x). E.g.f.: e^x+e^(6*x)+e^(7*x). [Mohammad K. Azarian, Dec 26 2008]
a(n) = 13*a(n-1) - 42*a(n-2) + 30, n>1. [Gary Detlefs, Jun 21 2010]
a(n) = A074619(n) + 1. - Michel Marcus, Nov 11 2013

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

Original entry on oeis.org

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)

cp's OEIS Frontend

A074511 a(n) = 1^n + 4^n + 5^n.

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A074516 a(n) = 1^n + 5^n + 6^n.

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Magma

Maple

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A074520 1^n + 6^n + 7^n.

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Maple

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

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Magma

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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

Formula

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