A195460 a(n) = 2^(2*n+1) - 3*2^n - 1.

1, 19, 103, 463, 1951, 7999, 32383, 130303, 522751, 2094079, 8382463, 33542143, 134193151, 536821759, 2147385343, 8589737983, 34359345151, 137438167039, 549754241023, 2199020109823, 8796086730751, 35184359505919, 140737463189503

Offset: 1

Author

Brad Clardy, Sep 18 2011

Keywords

• nonn
• easy

Comments

Binary numbers of the form (n)00(m) where n and m are the number of 1's, m is the index and n=m-1.

Examples

			First few terms in binary are 1, 10011, 1100111, 111001111, 11110011111, 1111100111111.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A052539, A103897, A195461 (prime values).

Programs

Magma

[2*4^n-3*2^n-1: n in [1..23]]; // Bruno Berselli, Sep 19 2011

PARI

a(n)=1<<(2*n+1)-3<Charles R Greathouse IV, Sep 19 2011

Formula

a(n) = 2*a(n-1)+A052539(n) = a(n-1)+A103897(n) for n>1.

G.f.: x*(1+12*x-16*x^2)/((1-x)*(1-2*x)*(1-4*x)). - Bruno Berselli, Sep 19 2011