A081186 -id:A081186 - cp's OEIS frontend

A087439 Expansion of (1-4x)/((1-x)(1-3x)(1-5x)).

1, 5, 22, 98, 451, 2135, 10312, 50468, 249061, 1235465, 6147802, 30650438, 152986471, 764135195, 3818284492, 19084248008, 95399716681, 476934013325, 2384476356382, 11921800651178, 59607259863691, 298031069141855

Offset: 0

Paul Barry, Sep 03 2003

Partial sums of A081186. The sequence 0,1,5,22,.. is given by 5^n/8+3^n/4-3/8. Binomial transform of A087440.

Index entries for linear recurrences with constant coefficients, signature (9,-23,15).

a(n)=5*5^n/8+3*3^n/4-3/8.

A346992 Numbers occurring as divisors of 3^k + 5^k.

Original entry on oeis.org

1, 2, 4, 8, 13, 17, 19, 23, 26, 29, 31, 34, 37, 38, 41, 46, 47, 53, 58, 62, 73, 74, 76, 79, 82, 83, 89, 92, 94, 97, 101, 106, 107, 113, 124, 137, 139, 146, 149, 151, 152, 157, 158, 166, 167, 169, 178, 184, 188, 193, 194, 199, 202, 211, 212, 214, 221, 226, 227

Offset: 1

Hugo Pfoertner, Aug 11 2021

nonn

If n is a term, then so are all divisors of n. - Robert Israel, Dec 08 2022

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A074606, A081186.

filter:= proc(n) local v;
   if igcd(n,15) <> 1 then return false fi;
   q:= 5/3 mod n;
   traperror(NumberTheory:-ModularLog(-1,q,n)) <> lasterror
end proc:
filter(1):= true:
select(filter, [$1..300]); # Robert Israel, Dec 08 2022

A152105 a(n) = (10^n + 6^n)/2.

Original entry on oeis.org

1, 8, 68, 608, 5648, 53888, 523328, 5139968, 50839808, 505038848, 5030233088, 50181398528, 501088391168, 5006530347008, 50039182082048, 500235092492288, 5001410554953728, 50008463329722368, 500050779978334208, 5000304679870005248, 50001828079220031488, 500010968475320188928

Offset: 0

Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008

Index entries for linear recurrences with constant coefficients, signature (16,-60).

Cf. A081186, A098158.

LinearRecurrence[{16,-60},{1,8},30] (* Harvey P. Dale, Jan 27 2015 *)

a(n) = (10^n + 6^n)/2. - Klaus Brockhaus, Nov 26 2008
From Philippe Deléham, Nov 26 2008: (Start)
a(n) = 16*a(n-1) - 60*a(n-2), n > 1; a(0)=1, a(1)=8.
G.f.: (1-8*x)/((1-6*x)*(1-10*x)).
a(n) = (Sum_{k=0..n} A098158(n,k)*2^(4*k))/2^n. (End)
a(n) = 2^n*A081186(n). - R. J. Mathar, Feb 04 2021
E.g.f.: exp(8*x)*cosh(2*x). - Elmo R. Oliveira, Aug 23 2024

Extended beyond a(6) by Klaus Brockhaus, Nov 26 2008

a(19)-a(21) from Elmo R. Oliveira, Aug 23 2024

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A087439 Expansion of (1-4x)/((1-x)(1-3x)(1-5x)).

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A346992 Numbers occurring as divisors of 3^k + 5^k.

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A152105 a(n) = (10^n + 6^n)/2.

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