A152775 -id:A152775 - cp's OEIS frontend

A152776 Numbers such that every run length in base 2 is 3.

7, 56, 455, 3640, 29127, 233016, 1864135, 14913080, 119304647, 954437176, 7635497415, 61083979320, 488671834567, 3909374676536, 31274997412295, 250199979298360, 2001599834386887, 16012798675095096, 128102389400760775

Offset: 1

Omar E. Pol, Jan 18 2009

a(n) is the number whose binary representation is A152775(n).

Zak Seidov, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (8, 1, -8).

Cf. A043291, A152775, A153435.

a(n)= 8*a(n-1) +a(n-2) -8*a(n-3). G.f.: 7x/((1-x)(1-8x)(1+x)). a(n)= (-7*(-1)^n-9+16*8^n)/18 = 7*A033118(n). [From R. J. Mathar, Jan 20 2009]

More terms from R. J. Mathar, Jan 20 2009

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

Original entry on oeis.org

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

Offset: 1

Omar E. Pol, Jan 25 2009

A154806 written in base 2.

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

Vincenzo Librandi, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (10000,1,-10000).

Cf. A152775, A153435, A154806, A154807.

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 *)

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

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)

A154807 Numbers with 5n binary digits where every run length is 5, written in binary.

Original entry on oeis.org

11111, 1111100000, 111110000011111, 11111000001111100000, 1111100000111110000011111, 111110000011111000001111100000, 11111000001111100000111110000011111, 1111100000111110000011111000001111100000, 111110000011111000001111100000111110000011111

Offset: 1

Omar E. Pol, Jan 25 2009

A154808 written in base 2.

			n ... a(n) ........................ A154808(n)
1 ... 11111 ....................... 31
2 ... 1111100000 .................. 992
3 ... 111110000011111 ............. 31775
4 ... 11111000001111100000 ........ 1016800
5 ... 1111100000111110000011111 ... 32537631

Vincenzo Librandi, Table of n, a(n) for n = 1..100
Index entries for linear recurrences with constant coefficients, signature (100000,1,-100000).

Cf. A152775, A153435, A154805, A154808.

CoefficientList[Series[11111/((x - 1) (x + 1) (100000 x - 1)), {x, 0, 10}], x] (* Vincenzo Librandi, Apr 22 2014 *)
LinearRecurrence[{100000,1,-100000},{11111,1111100000,111110000011111},20] (* Harvey P. Dale, Aug 08 2023 *)

Vec(11111*x/((x-1)*(x+1)*(100000*x-1)) + O(x^100)) \\ Colin Barker, Apr 20 2014

From Colin Barker, Apr 20 2014: (Start)
a(n) = (-100001-99999*(-1)^n+2^(6+5*n)*3125^(1+n))/1800018.
a(n) = 100000*a(n-1)+a(n-2)-100000*a(n-3).
G.f.: 11111*x / ((x-1)*(x+1)*(100000*x-1)). (End)

More terms from Colin Barker, Apr 20 2014

cp's OEIS Frontend

A152776 Numbers such that every run length in base 2 is 3.

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

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A154807 Numbers with 5n binary digits where every run length is 5, written in binary.

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