A001579 -id:A001579 - cp's OEIS frontend

A074502 a(n) = 1^n + 2^n + 6^n.

3, 9, 41, 225, 1313, 7809, 46721, 280065, 1679873, 10078209, 60467201, 362799105, 2176786433, 13060702209, 78364180481, 470185017345, 2821109972993, 16926659575809, 101559956930561, 609359740534785, 3656158441111553

Offset: 0

Robert G. Wilson v, Aug 23 2002

From Jonathan Vos Post, Apr 16 2005: (Start)
Primes in this sequence include: a(2) = 41, a(10) = 60467201, a(18) = 101559956930561, a(34) = 286511799958070449017978881, a(58) = 1357602166130257152481187563448636039086735361.
Semiprimes in this sequence include: a(1) = 9 = 3^2, a(4) = 1313 = 13 * 101, a(6) = 46721 = 19 * 2459, a(8) = 1679873 = 13 * 129221, a(12) = 2176786433 = 19 * 114567707, a(13) = 13060702209 = 3 * 4353567403, a(28) = 6140942214465083932673 = 13 * 472380170343467994821, a(29) = 36845653286789429854209 = 3 * 12281884428929809951403, a(72) = 106387358923716524807713475752456398462534338499504504833 = 59670762632990981 * 1782905969847563299479030657520813855693. (End)

Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

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

Table[1^n + 2^n + 6^n, {n, 0, 20}]
LinearRecurrence[{9,-20,12},{3,9,41},30] (* Harvey P. Dale, Aug 15 2017 *)

G.f.: 1/(1-x)+1/(1-2*x)+1/(1-6*x). E.g.f.: e^x+e^(2*x)+e^(6*x). [Mohammad K. Azarian, Dec 26 2008]

a(n) = 8*a(n-1) - 12*a(n-2) + 5, n> 1. [Gary Detlefs, Jun 21 2010]

A074515 a(n) = 1^n + 4^n + 9^n.

Original entry on oeis.org

3, 14, 98, 794, 6818, 60074, 535538, 4799354, 43112258, 387682634, 3487832978, 31385253914, 282446313698, 2541932937194, 22877060890418, 205892205836474, 1853024483819138, 16677198879535754, 150094704016475858

Offset: 0

Robert G. Wilson v, Aug 23 2002

Index entries for linear recurrences with constant coefficients, signature (14,-49,36).

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

Cf. A052539.

Table[1^n + 4^n + 9^n, {n, 0, 20}]
LinearRecurrence[{14,-49,36},{3,14,98},30] (* Harvey P. Dale, Aug 06 2013 *)

def a(n): return 1 + 4**n + 9**n
print([a(n) for n in range(19)]) # Michael S. Branicky, Mar 14 2021

From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-x) + 1/(1-4*x) + 1/(1-9*x).
E.g.f.: e^x + e^(4*x) + e^(9*x). (End)
a(n) = 13*a(n-1) - 36*a(n-2) + 24 with a(0)=3, a(1)=14. - Vincenzo Librandi, Jul 21 2010

A074535 a(n) = 2^n + 4^n + 8^n.

Original entry on oeis.org

3, 14, 84, 584, 4368, 33824, 266304, 2113664, 16843008, 134480384, 1074791424, 8594130944, 68736258048, 549822930944, 4398314962944, 35185445863424, 281479271743488, 2251816993685504, 18014467229220864, 144115462954287104

Offset: 0

Robert G. Wilson v, Aug 23 2002

Number of monic irreducible polynomials of degree 1 in GF(2^n)[x,y,z]. - Max Alekseyev, Jan 23 2006

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (14,-56,64).

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

[2^n + 4^n + 8^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Mathematica
```
Table[2^n + 4^n + 8^n, {n, 0, 20}]
```

def a(n): return 2**n + 4**n + 8**n
print([a(n) for n in range(20)]) # Michael S. Branicky, Mar 14 2021

G.f.: 1/(1-2*x)+1/(1-4*x)+1/(1-8*x). E.g.f.: exp(2*x)+exp(4*x)+exp(8*x). [Mohammad K. Azarian, Dec 26 2008]

Let A=[1, 1, 1;2, 0, -2;1, -1, 1], the 3 X 3 Krawtchouk matrix. Then a(n)=trace((A*A')^n). - Paul Barry, Sep 18 2004

A074579 a(n) = 6^n + 8^n + 9^n.

Original entry on oeis.org

3, 23, 181, 1457, 11953, 99593, 840241, 7160057, 61503553, 531715913, 4620992401, 40333791257, 353325795553, 3104682336233, 27353203130161, 241545689168057, 2137316275469953, 18945908172796553, 168210593763149521

Offset: 0

Robert G. Wilson v, Aug 23 2002

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (23,-174,432).

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

[6^n + 8^n + 9^n: n in [0..20]]; // Vincenzo Librandi, May 20 2011

Table[6^n + 8^n + 9^n, {n, 0, 20}]
LinearRecurrence[{23,-174,432},{3,23,181},30] (* Harvey P. Dale, Sep 20 2016 *)

From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-6*x) + 1/(1-8*x) + 1/(1-9*x).
E.g.f.: e^(6*x) + e^(8*x) + e^(9*x). (End)
a(n) = 23*a(n-1)-174*a(n-2)+432*a(n-3). - Wesley Ivan Hurt, Apr 17 2022

A074508 a(n) = 1^n + 3^n + 6^n.

Original entry on oeis.org

3, 10, 46, 244, 1378, 8020, 47386, 282124, 1686178, 10097380, 60525226, 362974204, 2177313778, 13062288340, 78368947066, 470199333484, 2821152954178, 16926788584900, 101560344088906, 609360902271964

Offset: 0

Robert G. Wilson v, Aug 23 2002

Index entries for linear recurrences with constant coefficients, signature (10,-27,18).

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

Mathematica
```
Table[1^n + 3^n + 6^n, {n, 0, 20}]
```

G.f.: 1/(1-x)+1/(1-3*x)+1/(1-6*x). E.g.f.: e^x+e^(3*x)+e^(6*x). [Mohammad K. Azarian, Dec 26 2008]

a(n) = 9*a(n-1) - 18*a(n-2) + 10, n>1. [Gary Detlefs, Jun 21 2010]

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

Original entry on oeis.org

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)

cp's OEIS Frontend

A074502 a(n) = 1^n + 2^n + 6^n.

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A074515 a(n) = 1^n + 4^n + 9^n.

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A074535 a(n) = 2^n + 4^n + 8^n.

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A074579 a(n) = 6^n + 8^n + 9^n.

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Magma

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A074508 a(n) = 1^n + 3^n + 6^n.

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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