A074603 -id:A074603 - cp's OEIS frontend

A155592 8^n+2^n-1^n.

1, 9, 67, 519, 4111, 32799, 262207, 2097279, 16777471, 134218239, 1073742847, 8589936639, 68719480831, 549755822079, 4398046527487, 35184372121599, 281474976776191, 2251799813816319, 18014398509744127, 144115188076380159

Offset: 0

Mohammad K. Azarian, Jan 24 2009

Index entries for linear recurrences with constant coefficients, signature (11,-26,16).

Cf. A074501, A074600, A005057, A005056, A099393, A155588, A155590.

Table[8^n+2^n-1^n,{n,0,30}] (* or *) LinearRecurrence[{11,-26,16},{1,9,67},30] (* Harvey P. Dale, Jul 09 2017 *)

a(n)=8^n+2^n-1 \\ Charles R Greathouse IV, Jun 11 2015

G.f.: 1/(1-8*x)+1/(1-2*x)-1/(1-x). E.g.f.: e^(8*x)+e^(2*x)-e^x.
a(n)=10*a(n-1)-16*a(n-2)-7 with a(0)=1, a(1)=9 - Vincenzo Librandi, Jul 21 2010
a(n) = A074603(n)-1. - R. J. Mathar, Mar 10 2022

A081342 a(n) = (8^n + 2^n)/2.

Original entry on oeis.org

1, 5, 34, 260, 2056, 16400, 131104, 1048640, 8388736, 67109120, 536871424, 4294968320, 34359740416, 274877911040, 2199023263744, 17592186060800, 140737488388096, 1125899906908160, 9007199254872064, 72057594038190080, 576460752303947776, 4611686018428436480

Offset: 0

Paul Barry, Mar 18 2003

Binomial transform of A034494.

5th binomial transform of {1, 0, 9, 0, 81, 0, 729, 0, ...}.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (10,-16).

Cf. A074603, A025551, A081343.

List([0..30], n-> (8^n + 2^n)/2); # G. C. Greubel, Jan 08 2020

[(8^n+2^n)/2: n in [0..30]]; // Vincenzo Librandi, Jun 13 2011

seq( (8^n + 2^n)/2, n=0..30); # G. C. Greubel, Jan 08 2020

Table[(8^n + 2^n)/2, {n, 0, 30}] (* Vladimir Joseph Stephan Orlovsky, Jun 12 2011 *)

a(n)=(8^n+2^n)/2 \\ Charles R Greathouse IV, Sep 28 2015

[(8^n + 2^n)/2 for n in (0..30)] # G. C. Greubel, Jan 08 2020

a(n) = (8^n + 2^n)/2.
a(n) = 10*a(n-1) - 16*a(n-2), a(0)=1, a(1)=5.
G.f.: (1-5*x)/((1-2*x)*(1-8*x)).
E.g.f.: exp(5*x)*cosh(3*x).
a(n) = ((5+sqrt(9))^n + (5-sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008
a(n) = A074603(n)/2. - Michel Marcus, Jan 09 2020

A045581 Numbers k that divide 8^k + 2^k.

Original entry on oeis.org

1, 2, 4, 5, 8, 16, 25, 32, 34, 64, 125, 128, 205, 256, 512, 578, 625, 1024, 1025, 1028, 2048, 2525, 3125, 4096, 5125, 8192, 8405, 9826, 10256, 12625, 15625, 16384, 25625, 32768, 42025, 63125, 65536, 78125, 103525, 128125, 131072, 167042, 168305

Offset: 1

David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..400

Cf. A074603.

Select[Range[200000], Divisible[PowerMod[2, #, #] + PowerMod[8, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *)

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A155592 8^n+2^n-1^n.

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A081342 a(n) = (8^n + 2^n)/2.

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A045581 Numbers k that divide 8^k + 2^k.

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