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A195156 a(n) = (16^n-1)/3. 2
0, 5, 85, 1365, 21845, 349525, 5592405, 89478485, 1431655765, 22906492245, 366503875925, 5864062014805, 93824992236885, 1501199875790165, 24019198012642645, 384307168202282325, 6148914691236517205, 98382635059784275285, 1574122160956548404565 (list; graph; refs; listen; history; text; internal format)
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

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..800

Index entries for linear recurrences with constant coefficients, signature (17,-16).

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)

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.

Cf. A000975, A001045.

Sequence in context: A201797 A012743 A139744 * A188918 A218139 A241330

Adjacent sequences:  A195153 A195154 A195155 * A195157 A195158 A195159

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

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Last modified September 17 19:16 EDT 2019. Contains 327137 sequences. (Running on oeis4.)