OFFSET
3,1
COMMENTS
Sequence appears to be 5*A000108 (with a different offset). - Peter Bala, Nov 26 2013
LINKS
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 09 2012
EXTENSIONS
a(11)-a(36) from Robert Price, Jun 03 2012
STATUS
approved