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

 

Logo

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 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A212344 Sequence of coefficients of x^(n-3) in marked mesh pattern generating function Q_{n,132}^(0,3,0,0)(x). 0
5, 5, 10, 25, 70, 210, 660, 2145, 7150, 24310, 83980, 293930, 1040060, 3714500, 13372200, 48474225, 176788350, 648223950, 2388193500, 8836315950, 32820602100, 122331335100, 457412818200, 1715298068250, 6449520736620, 24309732007260, 91836765360760 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

Sequence appears to be 5*A000108 (with a different offset). - Peter Bala, Nov 26 2013

LINKS

Table of n, a(n) for n=3..29.

S. Kitaev, J. Remmel and M. Tiefenbruck, Marked mesh patterns in 132-avoiding permutations I, arXiv preprint arXiv:1201.6243, 2012

FORMULA

Conjecture: (n-2)*a(n) = 2*(2n-7)*a(n-1). R. J. Mathar, Jun 27 2012

G.f.: conjecture: 5*T(0), where T(k) = 1 - x/( x - 1/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 26 2013

G.f.: conjecture: 5*(1-sqrt(1-4*x))/(2*x) = 10/T(0), where T(k) = 2*x*(2*k+1) + k+2 - 2*x*(k+2)*(2*k+3)/T(k+1); (continued fraction). - Sergei N. Gladkovskii, Nov 26 2013

MAPLE

A212344List := proc(m) local A, P, n; A := [5, 5]; P := [5];

for n from 1 to m - 2 do P := ListTools:-PartialSums([op(P), P[-1]]);

A := [op(A), P[-1]] od; A end: A212344List(27); # Peter Luschny, Mar 26 2022

MATHEMATICA

QQ0[t, x] = ( (1 - (1-4*x*t)^(1/2)) ) / (2*x*t); QQ1[t, x] = 1/(1 - t*QQ0[t, x]); QQ2[t, x] = (1 + t*(QQ1[t, x] - QQ0[t, x]))/(1 - t*QQ0[t, x]); QQ3[t, x] = (1 + t*(QQ2[t, x] - QQ0[t, x] + t*(QQ1[t, x] - QQ0[t, x])))/(1 - t*QQ0[t, x]); Simplify[Series[QQ3[t, x], {t, 0, 35}]] (* Robert Price, Jun 03 2012 *)

CROSSREFS

Sequence in context: A245418 A082450 A304266 * A298181 A290332 A302842

Adjacent sequences: A212341 A212342 A212343 * A212345 A212346 A212347

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, May 09 2012

EXTENSIONS

a(11)-a(36) from Robert Price, Jun 03 2012

STATUS

approved

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 30 02:32 EST 2022. Contains 358431 sequences. (Running on oeis4.)