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A154805 Numbers with 4n binary digits where every run length is 4, written in binary. 3
1111, 11110000, 111100001111, 1111000011110000, 11110000111100001111, 111100001111000011110000, 1111000011110000111100001111, 11110000111100001111000011110000, 111100001111000011110000111100001111 (list; graph; refs; listen; history; text; internal format)
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

AUTHOR

Omar E. Pol, Jan 25 2009

STATUS

approved

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Last modified October 22 06:02 EDT 2018. Contains 316432 sequences. (Running on oeis4.)