Displaying 11-13 of 13 results found.
Expansion of (1-4x)/((1-x)(1-3x)(1-5x)).
+10
1
1, 5, 22, 98, 451, 2135, 10312, 50468, 249061, 1235465, 6147802, 30650438, 152986471, 764135195, 3818284492, 19084248008, 95399716681, 476934013325, 2384476356382, 11921800651178, 59607259863691, 298031069141855
COMMENTS
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.
FORMULA
a(n)=5*5^n/8+3*3^n/4-3/8.
Numbers occurring as divisors of 3^k + 5^k.
+10
1
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
COMMENTS
If n is a term, then so are all divisors of n. - Robert Israel, Dec 08 2022
MAPLE
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:
1, 8, 68, 608, 5648, 53888, 523328, 5139968, 50839808, 505038848, 5030233088, 50181398528, 501088391168, 5006530347008, 50039182082048, 500235092492288, 5001410554953728, 50008463329722368, 500050779978334208, 5000304679870005248, 50001828079220031488, 500010968475320188928
FORMULA
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)
MATHEMATICA
LinearRecurrence[{16, -60}, {1, 8}, 30] (* Harvey P. Dale, Jan 27 2015 *)
AUTHOR
Al Hakanson (hawkuu(AT)gmail.com), Nov 24 2008
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