The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A115291

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A115291

Expansion of (1+x)^3/(1-x).
(history; published version)

#33 by Michael De Vlieger at Fri Aug 09 10:08:21 EDT 2024

STATUS

reviewed

approved

#32 by Andrew Howroyd at Fri Aug 09 09:05:38 EDT 2024

STATUS

proposed

reviewed

#31 by Elmo R. Oliveira at Fri Aug 09 06:06:26 EDT 2024

STATUS

editing

proposed

#30 by Elmo R. Oliveira at Fri Aug 09 06:03:15 EDT 2024

FORMULA

a(n) = 8 - C(2, n) - 2*C(1, n) - 4*C(0, n);.

a(n) = Sum_{k=0..n} C(3, k);.

From Elmo R. Oliveira, Aug 09 2024

E.g.f.: 8*exp(x) - 7 - 4*x - x^2/2.

a(n) = 8, n > 2. (End)

STATUS

approved

editing

#29 by Joerg Arndt at Wed Jun 01 01:52:30 EDT 2022

STATUS

reviewed

approved

#28 by Michel Marcus at Wed Jun 01 01:35:00 EDT 2022

STATUS

proposed

reviewed

#27 by Jon E. Schoenfield at Wed Jun 01 01:20:09 EDT 2022

STATUS

editing

proposed

#26 by Jon E. Schoenfield at Wed Jun 01 01:20:07 EDT 2022

COMMENTS

Let m=4. We observe that a(n) =sum Sum_{C(m,n-2*k),k=0..floor(n/2)} C(m,n-2*k). Then there is a link with A113311 and A040000: it is the same formula with respectively m=3 and m=2. We can generalize this result with the sequence whose G.f is given by (1+z)^(m-1)/(1-z). - Richard Choulet, Dec 08 2009

FORMULA

a(n) = 8 - C(2, n) - 2*C(1, n) - 4*C(0, n); a(n) = sum{k=0..n, C(3, k)}; a(n) = A004070(n, 3).

a(n) = Sum_{k=0..n} C(3, k);

a(n) = A004070(n, 3).

STATUS

proposed

editing

#25 by Eric Rowland at Wed Jun 01 01:12:14 EDT 2022

STATUS

editing

proposed

#24 by Eric Rowland at Wed Jun 01 01:12:12 EDT 2022

COMMENTS

Also continued fraction expansion of (132-sqrt(17))/103. -_ _Bruno Berselli_, Sep 23 2011

STATUS

approved

editing