A074608 -id:A074608 - cp's OEIS frontend

A081336 a(n) = (7^n + 3^n)/2.

1, 5, 29, 185, 1241, 8525, 59189, 412865, 2885681, 20186645, 141267149, 988751945, 6920909321, 48445302365, 339113927909, 2373787929425, 16616486808161, 116315321563685, 814206992665469, 5699448173817305, 39896134892198201

Offset: 0

Paul Barry, Mar 18 2003

Binomial transform of A081336.

5th binomial transform of (1,0,4,0,16,0,64,...).

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Yassine Otmani, The 2-Pascal Triangle and a Related Riordan Array, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 12.
Index entries for linear recurrences with constant coefficients, signature (10,-21).

Cf. A074608, A081337.

[(7^n+3^n)/2: n in [0..25]]; // Vincenzo Librandi, Aug 08 2013

CoefficientList[Series[(1 - 5 x) / ((1 - 3 x) (1 - 7 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Aug 08 2013 *)
LinearRecurrence[{10,-21},{1,5},30] (* Harvey P. Dale, Dec 07 2014 *)

a(n)=(7^n+3^n)/2 \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 10*a(n-1) - 21*a(n-2), a(0)=1, a(1)=5.
G.f.: (1-5*x)/((1-3*x)*(1-7*x)).
E.g.f.: exp(5*x) * cosh(2*x).
a(n) = A074608(n) / 2. - Michel Marcus, Oct 07 2015
a(n) = Sum_{k=0..n} A027907(n,2k)*4^k . - J. Conrad, Aug 24 2016

A245806 a(n) = 3^n + 10^n.

Original entry on oeis.org

2, 13, 109, 1027, 10081, 100243, 1000729, 10002187, 100006561, 1000019683, 10000059049, 100000177147, 1000000531441, 10000001594323, 100000004782969, 1000000014348907, 10000000043046721, 100000000129140163, 1000000000387420489, 10000000001162261467

Offset: 0

Vincenzo Librandi, Aug 04 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (13,-30).

Cf. 3^n+k^n: A034472 (k=1), A007689 (k=2), A008776 (k=3), A074605 (k=4), A074606 (k=5), A074607 (k=6), A074608 (k=7), A074609 (k=8), A074610 (k=9), this sequence (k=10).

Magma
```
[3^n+10^n: n in [0..25]];
```

I:=[2,13]; [n le 2 select I[n] else 13*Self(n-1)-30*Self(n-2): n in [1..25]];

Table[(3^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 13 x)/((1 - 3 x) (1 - 10 x)), {x, 0, 30}], x]

a(n)=3^n + 10^n \\ Charles R Greathouse IV, Aug 26 2014

G.f.: (2-13*x)/((1-3*x)(1-10*x)).
E.g.f.: e^(3*x) + e^(10*x).
a(n) = 13*a(n-1)-30*a(n-2) for n>1.
a(n) = A000244(n) + A011557(n). - Michel Marcus, Aug 04 2014

A245807 a(n) = 7^n + 10^n.

Original entry on oeis.org

2, 17, 149, 1343, 12401, 116807, 1117649, 10823543, 105764801, 1040353607, 10282475249, 101977326743, 1013841287201, 10096889010407, 100678223072849, 1004747561509943, 10033232930569601, 100232630513987207, 1001628413597910449, 10011398895185373143

Offset: 0

Vincenzo Librandi, Aug 04 2014

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (17,-70).

Cf. 7^n+k^n: A034491 (k=1), A074602 (k=2), A074608 (k=3), A074613 (k=4), A074616 (k=5), A074619 (k=6), A109808 (k=7), A074622 (k=8), A074623 (k=9), this sequence (k=10).

Magma
```
[7^n+10^n: n in [0..25]];
```

I:=[2,17]; [n le 2 select I[n] else 17*Self(n-1)-70*Self(n-2): n in [1..25]];

Table[(7^n + 10^n), {n, 0, 30}] (* or *) CoefficientList[Series[(2 - 17 x)/((1 - 7 x) (1 - 10 x)), {x, 0, 40}], x]

G.f.: (2-17*x)/((1-7*x)*(1-10*x)).
E.g.f.: e^(7*x) + e^(10*x).
a(n) = 17*a(n-1)-70*a(n-2).
a(n) = A000420(n) + A011557(n).

A045586 Numbers k that divide 7^k + 3^k.

Original entry on oeis.org

1, 2, 5, 25, 55, 58, 125, 155, 275, 605, 625, 775, 1265, 1375, 1682, 1705, 3025, 3125, 3875, 4805, 6325, 6655, 6875, 8525, 13915, 15125, 15625, 18755, 19375, 24025, 29095, 31625, 33275, 34375, 39215, 42625, 48778, 52855, 53882, 69575, 73205

Offset: 1

David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..500

Cf. A074608.

Select[Range[75000],Divisible[7^#+3^#,#]&] (* Harvey P. Dale, Apr 21 2019 *)
Select[Range[75000], Divisible[PowerMod[7, #, #] + PowerMod[3, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *)

A045593 Numbers k that divide 9^k + 4^k.

Original entry on oeis.org

1, 13, 169, 2197, 14209, 28561, 184717, 371293, 2401321, 4826809, 15530437, 31217173, 62748517, 130238329, 178895977, 201895681, 405823249, 815730721, 1693098277, 2325647701, 2422762381, 2624643853, 4286414821, 5275702237

Offset: 1

David W. Wilson

nonn

Cf. A074608.

A258340 a(n) = (7^n + 3^n - 2)/8.

Original entry on oeis.org

1, 7, 46, 310, 2131, 14797, 103216, 721420, 5046661, 35316787, 247187986, 1730227330, 12111325591, 84778481977, 593446982356, 4154121702040, 29078830390921, 203551748166367, 1424862043454326, 9974033723049550, 69818234317954651, 488727634995505957

Offset: 1

Edwin McCravy, Aug 05 2015

This sequence appeared on an test given to job interviewers.

Index entries for linear recurrences with constant coefficients, signature (11,-31,21).

Cf. A074608.

[(3^n+7^n-2)/8: n in [1..30]]; // Vincenzo Librandi, Aug 22 2015

Table[(7^n + 3^n - 2)/8, {n, 1, 30}] (* Bruno Berselli, Aug 24 2015 *)
LinearRecurrence[{11,-31,21},{1,7,46},30] (* Harvey P. Dale, May 01 2018 *)

first(m)=vector(m,i,(3^i+7^i-2)/8) \\ Anders Hellström, Aug 20 2015

[(7^n+3^n-2)/8 for n in (1..30)] # Bruno Berselli, Aug 24 2015

a(n) = (A074608(n) - 2)/8. - Michel Marcus, Aug 20 2015
G.f.: x*(1-4*x)/((1-x)*(1-3*x)*(1-7*x)). - Vincenzo Librandi, Aug 22 2015
a(n) = 11*a(n-1) - 31*a(n-2) + 21*a(n-3) with n>2, a(0)=0. - Bruno Berselli, Aug 24 2015
a(n) = Sum_{k=1..n} A027907(n,2k)*4^(k-1) . - J. Conrad, Aug 30 2016

cp's OEIS Frontend

A081336 a(n) = (7^n + 3^n)/2.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Formula

A245806 a(n) = 3^n + 10^n.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Magma

Mathematica

PARI

Formula

A245807 a(n) = 7^n + 10^n.

Views

Author

Keywords

Links

Crossrefs

Programs

Magma

Magma

Mathematica

Formula

A045586 Numbers k that divide 7^k + 3^k.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A045593 Numbers k that divide 9^k + 4^k.

Views

Author

Keywords

Crossrefs

A258340 a(n) = (7^n + 3^n - 2)/8.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

PARI

Sage

Formula