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 A079589 a(n) = C(5n+1,n). 2
 1, 6, 55, 560, 5985, 65780, 736281, 8347680, 95548245, 1101716330, 12777711870, 148902215280, 1742058970275, 20448884000160, 240719591939480, 2840671544105280, 33594090947249085, 398039194165652550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n) is the number of paths from (0,0) to (5n,n) taking north and east steps while avoiding exactly 2 consecutive north steps. - Shanzhen Gao, Apr 15 2010 REFERENCES Shanzhen Gao, Pattern Avoidance in Paths and Walks, in preparation [From Shanzhen Gao, Apr 15 2010] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA a(n) is asymptotic to c*sqrt(n)*(3125/256)^n with c=0.557.... [c = 5^(3/2)/(sqrt(Pi)*2^(7/2)) = 0.55753878629774... - Vaclav Kotesovec, Feb 14 2019] 8*n*(4*n+1)*(2*n-1)*(4*n-1)*a(n) -5*(5*n+1)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Jul 17 2014 G.f.: hypergeom([2/5, 3/5, 4/5, 6/5], [1/2, 3/4, 5/4], (3125/256)*x). - Robert Israel, Aug 07 2014 a(n) = [x^n] 1/(1 - x)^(2*(2*n+1)). - Ilya Gutkovskiy, Oct 10 2017 MAPLE seq(binomial(5*n+1, n), n=0..100); # Robert Israel, Aug 07 2014 MATHEMATICA Table[Binomial[5n+1, n], {n, 0, 20}] (* Harvey P. Dale, Jan 23 2011 *) PROG (Magma) [Binomial(5*n+1, n): n in [0..20]]; // Vincenzo Librandi, Aug 07 2014 CROSSREFS Cf. A052203. Sequence in context: A110431 A121661 A118836 * A006200 A243691 A151345 Adjacent sequences: A079586 A079587 A079588 * A079590 A079591 A079592 KEYWORD nonn AUTHOR Benoit Cloitre, Jan 26 2003 STATUS approved

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Last modified June 10 16:09 EDT 2023. Contains 363205 sequences. (Running on oeis4.)