A154805 Numbers with 4n binary digits where every run length is 4, written in binary.

1111, 11110000, 111100001111, 1111000011110000, 11110000111100001111, 111100001111000011110000, 1111000011110000111100001111, 11110000111100001111000011110000, 111100001111000011110000111100001111

Offset

1,1

Comments

A154806 written in base 2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (10000,1,-10000).

Formula

From Colin Barker, Apr 20 2014: (Start)

a(n) = (-10001-9999*(-1)^n+2^(5+4*n)*625^(1+n))/180018.

a(n) = 10000*a(n-1)+a(n-2)-10000*a(n-3).

G.f.: 1111*x / ((x-1)*(x+1)*(10000*x-1)). (End)

Example

n ... a(n) ................... A154806(n)
1 ... 1111 ................... 15
2 ... 11110000 ............... 240
3 ... 111100001111 ........... 3855
4 ... 1111000011110000 ....... 61680
5 ... 11110000111100001111 ... 986895

Mathematica

CoefficientList[Series[1111/((x - 1) (x + 1) (10000 x - 1)), {x, 0, 10}], x] (* Vincenzo Librandi, Apr 22 2014 *)
LinearRecurrence[{10000, 1, -10000}, {1111, 11110000, 111100001111}, 20] (* Harvey P. Dale, Jul 31 2017 *)

Prog

(PARI) Vec(1111*x/((x-1)*(x+1)*(10000*x-1)) + O(x^100)) \\ Colin Barker, Apr 20 2014

Crossrefs

Cf. A152775, A153435, A154806, A154807.

Sequence in context: A291945 A015292 A274831 * A203897 A236050 A213979

Adjacent sequences: A154802 A154803 A154804 * A154806 A154807 A154808

Keyword

easy,nonn,base

Author

Omar E. Pol, Jan 25 2009

Status

approved