A074501 -id:A074501 - cp's OEIS frontend

A074507 a(n) = 1^n + 3^n + 5^n.

3, 9, 35, 153, 707, 3369, 16355, 80313, 397187, 1972809, 9824675, 49005273, 244672067, 1222297449, 6108298595, 30531927033, 152630937347, 763068593289, 3815084686115, 19074648589593, 95370918425027, 476847618556329

Offset: 0

Robert G. Wilson v, Aug 23 2002

Harvey P. Dale, Table of n, a(n) for n = 0..1000
T. A. Gulliver, Divisibility of sums of powers of odd integers, Int. Math. For. 5 (2010) 3059-3066, eq. (6).
D. Suprijanto, I. W. Suwarno, Observation on Sums of Powers of Integers Divisible by 3k-1, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, 2211 - 2217.
Index entries for linear recurrences with constant coefficients, signature (9,-23,15).

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

Table[1^n + 3^n + 5^n, {n, 0, 22}]
LinearRecurrence[{9,-23,15},{3,9,35},30] (* Harvey P. Dale, Mar 02 2022 *)

a(n) = 1 + 3^n + 5^n; \\ Michel Marcus, Aug 07 2017

a(n) = 8*a(n-1) - 15*a(n-2) + 8.

G.f.: 1/(1-x)+1/(1-3*x)+1/(1-5*x). E.g.f.: e^x+e^(3*x)+e^(5*x). [Mohammad K. Azarian, Dec 26 2008]

A155589 a(n) = 6^n + 2^n - 1.

Original entry on oeis.org

1, 7, 39, 223, 1311, 7807, 46719, 280063, 1679871, 10078207, 60467199, 362799103, 2176786431, 13060702207, 78364180479, 470185017343, 2821109972991, 16926659575807, 101559956930559, 609359740534783, 3656158441111551, 21936950642475007, 131621703846461439

Offset: 0

Mohammad K. Azarian, Jan 24 2009

Paolo Xausa, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (9,-20,12).

Cf. A074501, A074600, A005057, A005056, A099393, A155588.

Table[6^n + 2^n - 1, {n, 0, 25}] (* Paolo Xausa, Jul 30 2024 *)

a(n)=6^n+2^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-6*x)+1/(1-2*x)-1/(1-x).
E.g.f.: exp(6*x)+exp(2*x)-exp(x).
a(n) = 8*a(n-1)-12*a(n-2)-5 with a(0) = 1, a(1) = 7. - Vincenzo Librandi, Jul 21 2010

A074528 a(n) = 2^n + 3^n + 6^n.

Original entry on oeis.org

3, 11, 49, 251, 1393, 8051, 47449, 282251, 1686433, 10097891, 60526249, 362976251, 2177317873, 13062296531, 78368963449, 470199366251, 2821153019713, 16926788715971, 101560344351049, 609360902796251

Offset: 0

Robert G. Wilson v, Aug 23 2002

From Álvar Ibeas, Mar 24 2015: (Start)
Number of isomorphism classes of 3-fold coverings of a connected graph with circuit rank n+1 [Kwak and Lee].
Number of orbits of the conjugacy action of Sym(3) on Sym(3)^(n+1) [Kwak and Lee, 2001].
(End)

J. H. Kwak and J. Lee, Enumeration of graph coverings, surface branched coverings and related group theory, in Combinatorial and Computational Mathematics (Pohang, 2000), ed. S. Hong et al., World Scientific, Singapore 2001, pp. 97-161. [Added by N. J. A. Sloane, Nov 12 2009]

Hakan Icoz, Table of n, a(n) for n = 0..1000 (terms 0..200 from Vincenzo Librandi)
M. W. Hero and J. F. Willenbring, Stable Hilbert series as related to the measurement of quantum entanglement, Discrete Math., 309 (2010), 6508-6514.
J. H. Kwak and J. Lee, Isomorphism classes of graph bundles. Can. J. Math., 42(4), 1990, pp. 747-761.
Index entries for linear recurrences with constant coefficients, signature (11,-36,36).

Cf. A001550, A001576, A034513, A001579, A074501-A074580.
A246985 is essentially identical.
Third row of A160449, shifted.

[2^n + 3^n + 6^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Table[2^n + 3^n + 6^n, {n, 0, 20}]
LinearRecurrence[{11,-36,36},{3,11,49},30] (* Harvey P. Dale, May 02 2016 *)

a(n)=2^n+3^n+6^n \\ Charles R Greathouse IV, Oct 07 2015

From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-2*x)+1/(1-3*x)+1/(1-6*x).
E.g.f.: exp(2*x) + exp(3*x) + exp(6*x). (End)
a(n) = 11*a(n-1) - 36*a(n-2) + 36*a(n-3). - Wesley Ivan Hurt, Aug 21 2020

A155595 11^n+2^n-1.

Original entry on oeis.org

1, 12, 124, 1338, 14656, 161082, 1771624, 19487298, 214359136, 2357948202, 25937425624, 285311672658, 3138428380816, 34522712152122, 379749833599624, 4177248169448418, 45949729863637696, 505447028499424842

Offset: 0

Mohammad K. Azarian, Jan 24 2009

Index entries for linear recurrences with constant coefficients, signature (14,-35,22).

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590, A155592, A155593, A155594.

a(n)=11^n+2^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-11*x)+1/(1-2*x)-1/(1-x). E.g.f.: e^(11*x)+e^(2*x)-e^x.

a(n)=13*a(n-1)-22*a(n-2)-10 with a(0)=1, a(1)=12 - Vincenzo Librandi, Jul 21 2010

A074506 a(n) = 1^n + 3^n + 4^n.

Original entry on oeis.org

3, 8, 26, 92, 338, 1268, 4826, 18572, 72098, 281828, 1107626, 4371452, 17308658, 68703188, 273218426, 1088090732, 4338014018, 17309009348, 69106897226, 276040168412, 1102998412178, 4408506864308, 17623567104026

Offset: 0

Robert G. Wilson v, Aug 23 2002

Bruno Berselli, Table of n, a(n) for n = 0..1000.
Index entries for linear recurrences with constant coefficients, signature (8,-19,12).

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

Equals A074605(n) + 1.

Table[1^n + 3^n + 4^n, {n, 0, 22}]
LinearRecurrence[{8,-19,12},{3,8,26},30] (* Harvey P. Dale, May 12 2025 *)

a(n) = 7*a(n-1) - 12*a(n-2) + 6 with a(0)=3, a(1)=8. - Vincenzo Librandi, Jul 19 2010
a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3). - R. J. Mathar, Jul 18 2010
From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-x) + 1/(1-3*x) + 1/(1-4*x).
E.g.f.: e^x + e^(3*x) + e^(4*x). (End)

A074526 a(n) = 2^n + 3^n + 4^n.

Original entry on oeis.org

3, 9, 29, 99, 353, 1299, 4889, 18699, 72353, 282339, 1108649, 4373499, 17312753, 68711379, 273234809, 1088123499, 4338079553, 17309140419, 69107159369, 276040692699, 1102999460753, 4408508961459, 17623571298329

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 (9,-26,24).

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

[2^n + 3^n + 4^n: n in [0..25]]; // Vincenzo Librandi, Jun 11 2011

Table[2^n + 3^n + 4^n, {n, 0, 23}]
LinearRecurrence[{9,-26,24},{3,9,29},30] (* Harvey P. Dale, Jun 14 2022 *)

From Mohammad K. Azarian, Dec 26 2008: (Start)
G.f.: 1/(1-2*x)+1/(1-3*x)+1/(1-4*x).
E.g.f.: exp(2*x)+exp(3*x)+exp(4*x). (End)

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

Original entry on oeis.org

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

cp's OEIS Frontend

A074507 a(n) = 1^n + 3^n + 5^n.

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A155589 a(n) = 6^n + 2^n - 1.

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A074528 a(n) = 2^n + 3^n + 6^n.

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A155595 11^n+2^n-1.

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A074506 a(n) = 1^n + 3^n + 4^n.

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A074526 a(n) = 2^n + 3^n + 4^n.

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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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