The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A153335 Number of zig-zag paths from top to bottom of an n X n square whose color is not that of the top right corner. 5
 0, 1, 2, 8, 18, 52, 116, 296, 650, 1556, 3372, 7768, 16660, 37416, 79592, 175568, 371034, 807604, 1697660, 3657464, 7654460, 16357496, 34106712, 72407728, 150499908, 317777032, 658707896, 1384524656, 2863150440, 5994736336 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Indranil Ghosh, Table of n, a(n) for n = 1..1000 Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation FORMULA a(n) = (n+1)2^(n-2) - 2(n-1)binomial(n-2,(n-2)/2) for n even, a(n) = (n+1)2^(n-2) - (n)binomial(n-1,(n-1)/2) for n odd. MATHEMATICA Table[If[Mod[n, 2]==0, (n+1)*2^(n-2)-2(n-1) Binomial[n-2, (n-2)/2], (n+1)*2^(n-2)-(n) Binomial[n-1, (n-1)/2]], {n, 1, 30}] (* Indranil Ghosh, Feb 19 2017 *) PROG (Python) import math def C(n, r): ....f=math.factorial ....return f(n)/f(r)/f(n-r) def A153335(n): ....if n%2==0: return str(int((n+1)*2**(n-2)-2*(n-1)*C(n-2, (n-2)/2))) ....else: return str(int((n+1)*2**(n-2)-(n)*C(n-1, (n-1)/2))) # Indranil Ghosh, Feb 19 2017 (PARI) a(n) = if (n % 2, (n+1)*2^(n-2) - n*binomial(n-1, (n-1)/2), (n+1)*2^(n-2) - 2*(n-1)*binomial(n-2, (n-2)/2)); \\ Michel Marcus, Feb 19 2017 CROSSREFS Cf. A102699, A153334, A153336, A153337, A153338. Sequence in context: A249763 A114723 A267638 * A119853 A136201 A058082 Adjacent sequences:  A153332 A153333 A153334 * A153336 A153337 A153338 KEYWORD easy,nonn AUTHOR Joseph Myers, Dec 24 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified September 21 07:28 EDT 2021. Contains 347596 sequences. (Running on oeis4.)