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A195156
a(n) = (16^n-1)/3.
6
0, 5, 85, 1365, 21845, 349525, 5592405, 89478485, 1431655765, 22906492245, 366503875925, 5864062014805, 93824992236885, 1501199875790165, 24019198012642645, 384307168202282325, 6148914691236517205, 98382635059784275285, 1574122160956548404565
OFFSET
0,2
COMMENTS
Numbers of A002450 that are multiples of 5. Also sequence found by reading the line from 0, in the direction 0, 5,..., in the square spiral whose edges are the Jacobsthal numbers A001045 and whose vertices are the numbers A000975. This is a semi-diagonal in the spiral.
In binary, these numbers are 101...01 (see A031982). - Alonso del Arte, May 20 2017
0 together with Jacobsthal numbers ending with the decimal digit 5. - Jianing Song, Aug 30 2022
FORMULA
From Bruno Berselli, Sep 19 2011: (Start)
G.f.: 5*x/((1-x)*(1-16*x)).
a(n) = A002450(2n) = (16^n-1)/3.
a(n) = 5*A131865(n-1) = a(n-1) + 5*A001025(n-1) = 16*a(n-1) + 5 for n > 0. (End)
From Jianing Song, Aug 30 2022: (Start)
a(n) = A001045(4*n).
a(n+1) - a(n) = 10*A013777(n-1) = 80*A001025(n-1) for n >= 1. (End)
E.g.f.: exp(x)*(exp(15*x) - 1)/3. - Stefano Spezia, Dec 17 2022
MAPLE
A195156:=n->(16^n-1)/3; seq(A195156(k), k=0..50); # Wesley Ivan Hurt, Oct 24 2013
MATHEMATICA
Table[(16^n - 1)/3, {n, 0, 63}] (* Wesley Ivan Hurt, Oct 24 2013 *)
PROG
(Magma) [(16^n-1)/3:n in [0..20]]; // Vincenzo Librandi, Sep 20 2011
(PARI) for(n=0, 50, print1((16^n - 1)/3, ", ")) \\ G. C. Greubel, Oct 11 2017
CROSSREFS
Bisection of A002450.
First quadrisection of Jacobsthal numbers A001045; the other quadrisections are A139792 (second), A144864 (third), and A141060 (fourth).
Sequence in context: A012743 A359234 A139744 * A188918 A349936 A218139
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 10 2011
EXTENSIONS
New sequence name suggested by Charles R Greathouse IV using Berselli's formula. - Sep 19 2011
STATUS
approved