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Revision History for A268407

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Showing entries 1-10 | older changes

A268407

Number of North-East lattice paths that do not bounce off the diagonal y = x to the right.
(history; published version)

#18 by Bruno Berselli at Tue Feb 07 02:48:48 EST 2017

STATUS

editing

approved

#17 by Bruno Berselli at Tue Feb 07 02:48:35 EST 2017

PROG

(Maxima) a(n):=sum((k+1)*fib(k)*binomial(2*n-k, n-k), k, 0, n)/(n+1)+binomial(2*n, n)/(n+1); /* _Vladimir Kruchinin_, Feb 27 2016 */

a(n):=sum((k+1)*fib(k)*binomial(2*n-k, n-k), k, 0, n)/(n+1)+binomial(2*n, n)/(n+1); /* Vladimir Kruchinin, Feb 27 2016 */

STATUS

proposed

editing

#16 by G. C. Greubel at Mon Feb 06 23:09:52 EST 2017

STATUS

editing

proposed

#15 by G. C. Greubel at Mon Feb 06 23:09:33 EST 2017

LINKS

G. C. Greubel, <a href="/A268407/b268407.txt">Table of n, a(n) for n = 0..1000</a>

FORMULA

a(n):= Sum_{k=0..n}((k+1)*fib(k)*binomial(2*n-k,n-k))/(n+1) + C(n), where fib(n) - Fibonacci numbers, C(n) - Catalan numbers. - Vladimir Kruchinin, Feb 27 2016

STATUS

approved

editing

#14 by Vaclav Kotesovec at Sun Feb 28 03:23:45 EST 2016

STATUS

proposed

approved

#13 by Vaclav Kotesovec at Sat Feb 27 06:14:21 EST 2016

STATUS

editing

proposed

#12 by Vaclav Kotesovec at Sat Feb 27 06:14:06 EST 2016

FORMULA

a(n) ~ 13*4^n/(sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Feb 27 2016

CROSSREFS

Cf. A000045, A000108.

STATUS

proposed

editing

#11 by Vladimir Kruchinin at Sat Feb 27 05:40:36 EST 2016

STATUS

editing

proposed

#10 by Vladimir Kruchinin at Sat Feb 27 05:40:17 EST 2016

FORMULA

a(n):=Sum_{k=0..n}((k+1)*fib(k)*binomial(2*n-k,n-k))/(n+1)+C(n), where fib(n) - Fibonacci numbers, C(n) - Catalan numbers. - Vladimir Kruchinin, Feb 27 2016

PROG

(Maxima)

a(n):=sum((k+1)*fib(k)*binomial(2*n-k, n-k), k, 0, n)/(n+1)+binomial(2*n, n)/(n+1); /* Vladimir Kruchinin, Feb 27 2016 */

CROSSREFS

Cf. A000045, A000108

STATUS

approved

editing

#9 by Bruno Berselli at Thu Feb 04 03:37:42 EST 2016

STATUS

reviewed

approved