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
Examples
n ... a(n) ................... A154806(n) 1 ... 1111 ................... 15 2 ... 11110000 ............... 240 3 ... 111100001111 ........... 3855 4 ... 1111000011110000 ....... 61680 5 ... 11110000111100001111 ... 986895
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..100
- Index entries for linear recurrences with constant coefficients, signature (10000,1,-10000).
Programs
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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 *) -
PARI
Vec(1111*x/((x-1)*(x+1)*(10000*x-1)) + O(x^100)) \\ Colin Barker, Apr 20 2014
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)
Comments