A188530 2^(2n+1)-5*2^(n-1)-1.

2, 21, 107, 471, 1967, 8031, 32447, 130431, 523007, 2094591, 8383487, 33544191, 134197247, 536829951, 2147401727, 8589770751, 34359410687, 137438298111, 549754503167, 2199020634111

Offset: 1

Author

Brad Clardy, Apr 03 2011

Keywords

• nonn
• easy

Comments

Starting with n=2, binary palindromic numbers of the form (n-1)010(n-1) where n is the index and the number of 1's

Examples

			first 6 term in binary starting with n=2 are 10101,1101011,111010111,11110101111,1111101011111,111111010111111
		

Links

• Index entries for linear recurrences with constant coefficients, signature (7,-14,8).

Crossrefs

Cf. A267705.

Programs

Mathematica

Table[2^(2n+1)-5 2^(n-1)-1,{n,20}] (* or *) Rest[CoefficientList[ Series[(x(-2-7x+12x^2))/((x-1)(2x-1)(4x-1)), {x,0,20}], x]]  (* Harvey P. Dale, Apr 19 2011 *)

Python

print([2*4**n - 5*2**(n-1) - 1 for n in range(1, 50)]) # Karl V. Keller, Jr., Jun 09 2022

Formula

a(n) = 2^(2n+1)-2^(n+1)-2^(n-1)-1.

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

a(n)= +7*a(n-1) -14*a(n-2) +8*a(n-3). G.f. ( x*(-2-7*x+12*x^2) ) / ( (x-1)*(2*x-1)*(4*x-1) ). - R. J. Mathar, Apr 04 2011

a(n) = 2*4^n - 5*2^(n-1) - 1. - Karl V. Keller, Jr., Jun 09 2022