A074601 -id:A074601 - cp's OEIS frontend

A074600 a(n) = 2^n + 5^n.

2, 7, 29, 133, 641, 3157, 15689, 78253, 390881, 1953637, 9766649, 48830173, 244144721, 1220711317, 6103532009, 30517610893, 152587956161, 762939584197, 3814697527769, 19073486852413, 95367432689201, 476837160300277

Offset: 0

Robert G. Wilson v, Aug 25 2002

Digital root of a(n) is A010697(n). - Peter M. Chema, Oct 24 2016

Miller, Steven J., ed. Benford's Law: Theory and Applications. Princeton University Press, 2015. See page 14.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
D. Suprijanto, I. W. Suwarno, Observation on Sums of Powers of Integers Divisible by 3k-1, Applied Mathematical Sciences, Vol. 8, 2014, no. 45, pp. 2211-2217.
Index entries for linear recurrences with constant coefficients, signature (7,-10).

Cf. A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074601-A074624, A010697, A094475, A337429.

[2^n + 5^n: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

Table[2^n + 5^n, {n, 0, 25}]
LinearRecurrence[{7,-10},{2,7},30] (* Harvey P. Dale, May 09 2019 *)

a(n)=2^n+5^n \\ Charles R Greathouse IV, Sep 24 2015

a(n) = 5*a(n-1)-3*2^(n-1) = 7*a(n-1)- 10*a(n-2). [Corrected by Zak Seidov, Oct 24 2009]

G.f.: 1/(1-2*x)+1/(1-5*x). E.g.f.: e^(2*x)+e^(5*x). - Mohammad K. Azarian, Jan 02 2009

A092807 Expansion of (1-6x+4x^2)/((1-2x)(1-6*x)).

Original entry on oeis.org

1, 2, 8, 40, 224, 1312, 7808, 46720, 280064, 1679872, 10078208, 60467200, 362799104, 2176786432, 13060702208, 78364180480, 470185017344, 2821109972992, 16926659575808, 101559956930560, 609359740534784

Offset: 0

Paul Barry, Mar 06 2004

Second binomial transform of A054881 (closed walks at a vertex of an octahedron) With interpolated zeros, counts closed walks of length n at a vertex of the edge-vertex incidence graph of K_4 associated with the edges of K_4.

This also gives the number of noncrossing, nonnesting, 2-colored permutations on {1, 2, ..., n}. - Lily Yen, Apr 22 2013

G. C. Greubel, Table of n, a(n) for n = 0..1000
Lily Yen, Crossings and Nestings for Arc-Coloured Permutations, arXiv:1211.3472 [math.CO], 2012-2013 and Arc-coloured permutations, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754.
Lily Yen, Crossings and Nestings for Arc-Coloured Permutations and Automation, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.
Index entries for linear recurrences with constant coefficients, signature (8,-12).

Cf. A054881, A074601, A092803, A124302.

[1] cat [6^(n-1) + 2^(n-1): n in [1..40]]; // G. C. Greubel, Jan 04 2023

CoefficientList[Series[(1-6x+4x^2)/((1-2x)(1-6x)),{x,0,40}],x] (* or *) LinearRecurrence[{8,-12},{1,2,8},41] (* Harvey P. Dale, Aug 23 2011 *)

[(6^n + 3*2^n + 2*0^n)/6 for n in range(41)] # G. C. Greubel, Jan 04 2023

G.f.: (1-6*x+4*x^2)/((1-2*x)*(1-6*x)).
a(n) = (6^n + 3*2^n + 2*0^n)/6.
a(n) = A074601(n-1), n>0. - R. J. Mathar, Sep 08 2008
a(0)=1, a(1)=2, a(2)=8, a(n) = 8*a(n-1)-12*a(n-2). - Harvey P. Dale, Aug 23 2011
a(n) = A124302(n)*2^n. - Philippe Deléham, Nov 01 2011
E.g.f.: (1/6)*( 1 + 3*exp(2*x) + exp(6*x) ). - G. C. Greubel, Jan 04 2023

A045579 Numbers k that divide 6^k + 2^k.

Original entry on oeis.org

1, 2, 4, 8, 10, 16, 32, 50, 64, 128, 136, 164, 250, 256, 512, 1024, 1250, 1544, 2048, 2312, 4096, 5050, 6250, 6724, 8192, 11810, 16384, 25250, 26248, 31250, 32768, 32896, 39304, 59050, 65536, 126250, 131072, 156250, 262144, 275684, 295250, 297992, 376708, 446216

Offset: 1

David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..150

Cf. A074601.

Select[Range[300000], Divisible[PowerMod[2, #, #] + PowerMod[6, #, #], #] &] (* Amiram Eldar, Oct 23 2021 *)

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A074600 a(n) = 2^n + 5^n.

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A092807 Expansion of (1-6x+4x^2)/((1-2x)(1-6*x)).

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A045579 Numbers k that divide 6^k + 2^k.

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cp's OEIS Frontend

A074600 a(n) = 2^n + 5^n.

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Magma

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A092807 Expansion of (1-6*x+4*x^2)/((1-2*x)*(1-6*x)).

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Magma

Mathematica

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A045579 Numbers k that divide 6^k + 2^k.

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Author

Keywords

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Mathematica

A092807 Expansion of (1-6x+4x^2)/((1-2x)(1-6*x)).