A034513 -id:A034513 - cp's OEIS frontend

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

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

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)

A034661 Sum of n-th powers of divisors of 18.

Original entry on oeis.org

6, 39, 455, 6813, 112931, 1956669, 34591115, 617285253, 11064693731, 198756808749, 3574014537275, 64300154115093, 1157115988280531, 20825519793796029, 374836322743499435, 6746846977808919333

Offset: 0

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n=0..200
Index entries for linear recurrences with constant coefficients, signature (39,-533,3285,-9594,12636,-5832).

[DivisorSigma(n, 18): n in [0..20]]; // Bruno Berselli, Apr 05 2013 (improved MAGMA code by Vincenzo Librandi, Apr 17 2014)

Join[{6}, LinearRecurrence[{39, -533, 3285, -9594, 12636, -5832}, {39, 455, 6813, 112931, 1956669, 34591115}, 15]] (* Bruno Berselli, Apr 05 2013 *)
Table[(2^n + 1) (3^n + 9^n + 1), {n, 0, 15}] (* Bruno Berselli, Apr 05 2013 *)
Total[#^Range[0, 20]&/@Divisors[18]] (* Vincenzo Librandi, Apr 17 2014 *)

[sigma(18,n)for n in range(0,16)] # [Zerinvary Lajos, Jun 04 2009]

From Philippe Deléham, Apr 04 2013: (Start)
G.f.: 1/(1-x) + 1/(1-2*x) + 1/(1-3*x) + 1/(1-6*x) + 1/(1-9*x) + 1/(1-18*x).
a(n) = A000051(n)*A034513(n) = (2^n+1)*(3^n+9^n+1).
a(n) = 39*a(n-1) -533*a(n-2) +3285*a(n-3) -9594*a(n-4) +12636*a(n-5) -5832*a(n-6) with n>6, a(0)=6, a(1)=39, a(2)=455, a(3)=6813, a(4)= 112931, a(5)=1956669, a(6)=34591115. (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

A224384 a(n) = 1 + 17^n.

Original entry on oeis.org

2, 18, 290, 4914, 83522, 1419858, 24137570, 410338674, 6975757442, 118587876498, 2015993900450, 34271896307634, 582622237229762, 9904578032905938, 168377826559400930, 2862423051509815794, 48661191875666868482, 827240261886336764178, 14063084452067724991010

Offset: 0

Philippe Deléham, Apr 05 2013

Sum of n-th powers of divisors of 17.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (18,-17).

Cf. A001026.

17^Range[0,20]+1 (* Harvey P. Dale, Jul 19 2019 *)

a(n) = A001026(n) + 1.
G.f.: 1/(1-x) + 1/(1-17*x).
E.g.f.: exp(x) + exp(17*x).
a(n) = 18*a(n-1) - 17*a(n-2) with a(0) = 2, a(1) = 18.

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]

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

References

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Mathematica

Formula

A034661 Sum of n-th powers of divisors of 18.

Views

Author

Keywords

Links

Programs

Magma

Mathematica

Sage

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Python

Formula

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

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

Python

Formula

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

Views

Author

Keywords

Links