The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A113179 Expansion of 1/sqrt((1-2x)^2-8x^3). 2

%I #13 Aug 19 2022 04:20:06

%S 1,2,4,12,40,128,408,1328,4384,14560,48576,162816,547936,1850048,

%T 6263680,21257856,72298240,246345728,840775424,2873802240,9835840512,

%U 33704557568,115622041600,397032488960,1364610270720,4694145256448

%N Expansion of 1/sqrt((1-2x)^2-8x^3).

%C In general, 1/sqrt((1-a*x)^2-4*b*x^3) expands to sum{k=0..floor(n/2), C(n-k,k)C(n-2k,k)b^k*a^(n-3k)}.

%H Michael De Vlieger, <a href="/A113179/b113179.txt">Table of n, a(n) for n = 0..1837</a>

%H Hacène Belbachir, Abdelghani Mehdaoui, László Szalay, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL22/Szalay/szalay42.html">Diagonal Sums in the Pascal Pyramid, II: Applications</a>, J. Int. Seq., Vol. 22 (2019), Article 19.3.5.

%F a(n)=sum{k=0..floor(n/2), C(n-k, k)C(n-2k, k)2^(n-2k)}.

%F D-finite with recurrence: n*a(n) +2*(-2*n+1)*a(n-1) +4*(n-1)*a(n-2) +4*(-2*n+3)*a(n-3)=0. [Belbachir]

%t CoefficientList[Series[1/Sqrt[(1-2x)^2-8x^3],{x,0,30}],x] (* _Harvey P. Dale_, Dec 23 2017 *)

%Y Cf. A098479.

%K easy,nonn

%O 0,2

%A _Paul Barry_, Oct 16 2005

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

Last modified December 9 12:57 EST 2023. Contains 367690 sequences. (Running on oeis4.)