A147539 Numbers whose binary representation is the concatenation of n 1's, 2n-1 digits 0 and n 1's.

5, 99, 1799, 30735, 507935, 8257599, 133169279, 2139095295, 34292630015, 549218943999, 8791798056959, 140703128621055, 2251524935786495, 36026597995724799, 576443160117411839, 9223231299366486015

Offset: 1

Author

Omar E. Pol, Nov 06 2008

Keywords

• base
• easy
• nonn

Comments

a(n) is the number whose binary representation is A138120(n).

Links

• G. C. Greubel, Table of n, a(n) for n = 1..800
• Index entries for linear recurrences with constant coefficients, signature (27,-202,432,-256).

Crossrefs

Cf. A138120.

Programs

GAP

List([1..20], n-> 2^(4*n-1) -2^(3*n-1) +2^n -1); # G. C. Greubel, Jan 12 2020

Magma

[2^n-1+2^(4*n-1)-2^(3*n-1) : n in [1..20]]; // Wesley Ivan Hurt, Jan 11 2017

Maple

A147539:=n->2^n-1+2^(4*n-1)-2^(3*n-1): seq(A147539(n), n=1..30); # Wesley Ivan Hurt, Jan 11 2017

Mathematica

Table[FromDigits[Join[Table[1, {n}], Table[0, {2n - 1}], Table[1, {n}]], 2], {n, 1, 20}] (* Stefan Steinerberger, Nov 11 2008 *)
LinearRecurrence[{27,-202,432,-256},{5,99,1799,30735},20] (* Harvey P. Dale, Aug 28 2017 *)

PARI

vector(20, n, 2^(4*n-1) -2^(3*n-1) +2^n -1) \\ G. C. Greubel, Jan 12 2020

Sage

[2^(4*n-1) -2^(3*n-1) +2^n -1 for n in (1..20)] # G. C. Greubel, Jan 12 2020

Formula

a(n) = 2^n - 1 + 2^(4*n-1) - 2^(3*n-1). - R. J. Mathar, Nov 09 2008

G.f.: x*(5 -36*x +136*x^2)/((1-x)*(1-2*x)*(1-8*x)*(1-16*x)). - Colin Barker, Nov 04 2012

a(n) = 27*a(n-1) - 202*a(n-2) + 432*a(n-3) - 256*a(n-4). - Wesley Ivan Hurt, Jan 11 2017

Extensions

Extended by R. J. Mathar and Stefan Steinerberger, Nov 09 2008