User Name Remember Me? Password

 Number Theory Number Theory Math Forum

 July 3rd, 2018, 01:07 AM #1 Senior Member   Joined: Nov 2011 Posts: 250 Thanks: 3 Numeric sequence I have a numeric sequence: l(n)=sum[from k=1 to n](4k-1)*l(n-k) l(0)=1 Is there a function f(x) that satisfies l(n)? And if so, what is it? Last edited by skipjack; July 3rd, 2018 at 09:01 PM. July 3rd, 2018, 03:13 PM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 I'm not sure what you mean by "a function f(x) that satisfies l(n). Since that formula is "well defined", of course there exist a function defined on the positive integers that satisfies that formula. l(0)= 1 so $\displaystyle l(1)= (4- 1)l(0)= 3$ $\displaystyle l(2)= (4- 1)l(1)+ (8- 1)l(0)= 3(3)+ 7(1)= 16$ $\displaystyle l(3)= (4- 1)l(2)+ (8- 1)l(1)+ (12- 1)l(0)= 4(16)+ 7(3)+ 11(1)= 64+ 21+ 11= 96$ $\displaystyle l(4)= (4- 1)l(3)+ (8- 1)l(2)+ (12- 1)l(1)+ (16- 1)l(0)= 3(96)+ 7(16)+ 11(3)+ 15(1)= 288+ 112+ 33+ 15= 448$. Continue. No simple formula jumps out at me. Last edited by skipjack; July 3rd, 2018 at 09:48 PM. July 3rd, 2018, 09:48 PM #3 Global Moderator   Joined: Dec 2006 Posts: 21,020 Thanks: 2255 You should have had "3(16)" instead of "4(16)", which means that l(3) = 80, l(4) = 3(80) + 7(16) + 11(3) + 15(1) = 400, etc. That is, l(1) = 3, l(2+m) = 16*5^m for m = 0, 1, 2, etc. Tags number, numeric, sequence, theory Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Inflekx12 Algebra 3 February 19th, 2016 05:20 PM Guatama Number Theory 22 April 22nd, 2013 04:39 AM proglote Number Theory 3 October 30th, 2011 04:20 PM webmastermath Number Theory 5 July 7th, 2011 02:42 PM sivela Number Theory 3 May 10th, 2010 07:43 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top      