A231643 a(n) = 5*2^n + 5.

10, 15, 25, 45, 85, 165, 325, 645, 1285, 2565, 5125, 10245, 20485, 40965, 81925, 163845, 327685, 655365, 1310725, 2621445, 5242885, 10485765, 20971525, 41943045, 83886085, 167772165, 335544325, 671088645, 1342177285, 2684354565, 5368709125, 10737418245

Offset: 0

Author

Przemyslaw Wcislo, Nov 12 2013

Keywords

• nonn
• easy

Comments

For n > 2, decimals given by base 2 pattern: 101...zeros...101.

The ratio between a(n) and a(n+1) tends to 1/2.

Sum(1/a(i), i=0..infinity) = ( psi_2^(0)( 1 - i*Pi/log(2) ) + i*Pi ) / log(32) = 0.252899956069688841838263949451..., where psi_q^(m)(.) is the m-th derivative of the q-digamma function. [Bruno Berselli, Nov 15 2013]

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-2).

Crossrefs

Cf. A000079 (powers of 2), A000051.

Programs

Mathematica

Table[5*2^n + 5, {n, 0, 50}] (* T. D. Noe, Nov 15 2013 *)

Formula

a(n) = 5*A000051(n). - Philippe Deléham, Nov 15 2013

G.f.: 5*(2-3*x)/((1-x)*(1-2*x)). - Philippe Deléham, Nov 15 2013

a(n) = 3*a(n-1)-2*a(n-2) for n>1, a(0)=10, a(1)=15. - Philippe Deléham, Nov 15 2013