A034513 -id:A034513 - cp's OEIS frontend

A074557 3^n + 6^n + 9^n.

3, 18, 126, 972, 7938, 67068, 578826, 5065092, 44732898, 397517868, 3547309626, 31744033812, 284606850258, 2554928116668, 22955161402026, 206361331428132, 1855841341806018, 16694108488251468, 150196195641088026

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 (18,-99,162).

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

[3^n + 6^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 24 2011

Mathematica
```
Table[3^n + 6^n + 9^n, {n, 0, 20}]
```

G.f.: 1/(1-3*x)+1/(1-6*x)+1/(1-9*x). E.g.f.: exp(3*x)+exp(6*x)+exp(9*x). [From Mohammad K. Azarian, Dec 30 2008]

A074558 a(n) = 3^n + 7^n + 8^n.

Original entry on oeis.org

3, 18, 122, 882, 6578, 49818, 380522, 2922882, 22548578, 174591018, 1356276122, 10567438482, 82561295378, 646646418618, 5076274366922, 39931947947682, 314707950326978, 2484430456812618, 19642812494812922, 155514084423490482

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 (18,-101,168).

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

[3^n + 7^n + 8^n: n in [0..20]]; // Vincenzo Librandi, Aug 24 2011

Table[3^n + 7^n + 8^n, {n, 0, 20}]
LinearRecurrence[{18,-101,168},{3,18,122},20] (* Harvey P. Dale, Jan 21 2024 *)

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-7*x) + 1/(1-8*x).
E.g.f.: exp(3*x) + exp(7*x) + exp(8*x). (End)

A074559 a(n) = 3^n + 7^n + 9^n.

Original entry on oeis.org

3, 19, 139, 1099, 9043, 76099, 649819, 5608699, 48818083, 427793779, 3769318699, 33358563499, 296271355123, 2638756433059, 23555020310779, 210638707953499, 1886253162468163, 16909812342793939, 151723049282330059

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 (19,-111,189).

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

[3^n + 7^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 24 2011

Mathematica
```
Table[3^n + 7^n + 9^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-7*x) + 1/(1-9*x).
E.g.f.: exp(3*x) + exp(7*x) + exp(9*x). (End)
a(n) = 19*a(n-1) - 111*a(n-2) + 189*a(n-3). - Wesley Ivan Hurt, Apr 11 2023

A074560 a(n) = 3^n + 8^n + 9^n.

Original entry on oeis.org

3, 20, 154, 1268, 10738, 92060, 794314, 6882308, 59830498, 521657900, 4560585274, 39971171348, 351149544658, 3091623236540, 27274843749034, 241075518532388, 2134495208609218, 18928981642491980, 168109034193901594, 1494966906911109428, 13310586967150560178

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 (20,-123,216).

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

[3^n + 8^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 24 2011

A074560:=n->3^n + 8^n + 9^n: seq(A074560(n), n=0..25); # Wesley Ivan Hurt, Aug 15 2016

Table[3^n + 8^n + 9^n, {n, 0, 20}]
LinearRecurrence[{20,-123,216}, {3, 20, 154}, 25] (* G. C. Greubel, Aug 15 2016 *)

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-3*x) + 1/(1-8*x) + 1/(1-9*x).
E.g.f.: exp(3*x) + exp(8*x) + exp(9*x). (End)
a(n) = 20*a(n-1) - 123*a(n-2) + 216*a(n-3) for n>2. - Wesley Ivan Hurt, Aug 15 2016

A074561 a(n) = 4^n + 5^n + 6^n.

Original entry on oeis.org

3, 15, 77, 405, 2177, 11925, 66377, 374445, 2135777, 12292965, 71280377, 415819485, 2437700177, 14348506005, 84736115177, 501776304525, 2977992765377, 17706778767045, 105443373410777, 628708104245565

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 (15,-74,120).

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

[4^n + 5^n + 6^n: n in [0..20]]; // Vincenzo Librandi, Aug 24 2011

Mathematica
```
Table[4^n + 5^n + 6^n, {n, 0, 19}]
```

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-5*x) + 1/(1-6*x).
E.g.f.: exp(4*x) + exp(5*x) + exp(6*x). (End)

A074562 a(n) = 4^n + 5^n + 7^n.

Original entry on oeis.org

3, 16, 90, 532, 3282, 20956, 137370, 918052, 6220962, 42568876, 293289450, 2030349172, 14102205042, 98176822396, 684595023930, 4779152829892, 33389813427522, 233410633309516, 1632297014652810, 11418243549608212

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 (16,-83,140).

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

[4^n + 5^n + 7^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011

Mathematica
```
Table[4^n + 5^n + 7^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-5*x) + 1/(1-7*x).
E.g.f.: exp(4*x) + exp(5*x) + exp(7*x). (End)

A074563 a(n) = 4^n + 5^n + 8^n.

Original entry on oeis.org

3, 17, 105, 701, 4977, 36917, 281865, 2191661, 17233377, 136432997, 1084556025, 8642957021, 68980394577, 551043625877, 4404418462185, 35215963408781, 281631859568577, 2252579933007557, 18018281926224345, 144134536440090941

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 (17,-92,160).

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

[4^n + 5^n + 8^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011

Mathematica
```
Table[4^n + 5^n + 8^n, {n, 0, 20}]
```

vector(20, n, n--; 4^n + 5^n + 8^n) \\ G. C. Greubel, Nov 09 2018

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-5*x) + 1/(1-8*x).
E.g.f.: exp(4*x) + exp(5*x) + exp(8*x). (End)

A074564 a(n) = 4^n + 5^n + 9^n.

Original entry on oeis.org

3, 18, 122, 918, 7442, 63198, 551162, 4877478, 43502882, 389635758, 3497598602, 31434082038, 282690454322, 2543153640318, 22883164406042, 205922723414598, 1853177071709762, 16677961818988878, 150098518713741482

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 (18,-101,180).

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

[4^n + 5^n + 9^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011

Mathematica
```
Table[4^n + 5^n + 9^n, {n, 0, 20}]
```

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-5*x) + 1/(1-9*x).
E.g.f.: exp(4*x) + exp(5*x) + exp(9*x). (End)

A074565 a(n) = 4^n + 6^n + 7^n.

Original entry on oeis.org

3, 17, 101, 623, 3953, 25607, 168401, 1119863, 7509953, 50693447, 343990001, 2344318103, 16034846753, 110016813287, 756855672401, 5218820236343, 36058335444353, 249574353301127, 1730042274055601, 12008529803290583

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 (17,-94,168).

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

[4^n + 6^n + 7^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011

Table[4^n + 6^n + 7^n, {n, 0, 20}]
LinearRecurrence[{17,-94,168},{3,17,101},30] (* Harvey P. Dale, Jun 22 2013 *)

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-6*x) + 1/(1-7*x).
E.g.f.: exp(4*x) + exp(6*x) + exp(7*x). (End)
a(n) = 17*a(n-1) - 94*a(n-2) + 168*a(n-3); a(0)=3, a(1)=17, a(2)=101. - Harvey P. Dale, Jun 22 2013

A074566 a(n) = 4^n + 6^n + 8^n.

Original entry on oeis.org

3, 18, 116, 792, 5648, 41568, 312896, 2393472, 18522368, 144557568, 1135256576, 8956925952, 70913036288, 562883616768, 4476679110656, 35655630815232, 284300381585408, 2268743652999168, 18116027185627136, 144724822693773312

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 (18,-104,192).

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

[4^n + 6^n + 8^n: n in [0..20]]; // Vincenzo Librandi, Aug 25 2011

Table[4^n + 6^n + 8^n, {n, 0, 20}]
LinearRecurrence[{18,-104,192},{3,18,116},20] (* Harvey P. Dale, Oct 16 2023 *)

From Mohammad K. Azarian, Dec 30 2008: (Start)
G.f.: 1/(1-4*x) + 1/(1-6*x) + 1/(1-8*x).
E.g.f.: exp(4*x) + exp(6*x) + exp(8*x). (End)

cp's OEIS Frontend

A074557 3^n + 6^n + 9^n.

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Magma

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A074558 a(n) = 3^n + 7^n + 8^n.

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Magma

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A074559 a(n) = 3^n + 7^n + 9^n.

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Magma

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A074560 a(n) = 3^n + 8^n + 9^n.

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Magma

Maple

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A074561 a(n) = 4^n + 5^n + 6^n.

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Magma

Mathematica

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A074562 a(n) = 4^n + 5^n + 7^n.

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Magma

Mathematica

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A074563 a(n) = 4^n + 5^n + 8^n.

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Magma

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PARI

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A074564 a(n) = 4^n + 5^n + 9^n.

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