login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A298300 Analog of Motzkin numbers for Coxeter type D. 1
1, 4, 11, 31, 87, 246, 699, 1996, 5723, 16468, 47533, 137567, 399073, 1160082, 3378483, 9855207, 28790403, 84218052, 246651729, 723165765, 2122391109, 6234634266, 18330019029, 53932825926, 158802303429, 467898288676, 1379485436579, 4069450219561 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,2

LINKS

Table of n, a(n) for n=2..29.

FORMULA

a(n) = A002426(n-1) + A290380(n) (the latter being extended by A290380(2)=0).

Conjectural algebraic equation: 3*t+2+(3*t^2+5*t-2)*f(t)+(3*t^3-t^2)*f(t)^2 = 0.

From Peter Luschny, Jan 23 2018: (Start)

a(n) = hypergeom([(1-n)/2,1-n/2],[1],4]+(n-2)*hypergeom([1-n/2,3/2-n/2],[2],4).

a(n) = G(n-1,1-n,-1/2) + G(n-2,1-n,-1/2)*(n-2)/(n-1) where G(n,a,x) denotes the n-th Gegenbauer polynomial. (End)

MATHEMATICA

b[n_] := Hypergeometric2F1[(1 - n)/2, 1 - n/2, 1, 4];

c[n_] := (n-2) Hypergeometric2F1[1 - n/2, 3/2 - n/2, 2, 4];

Table[b[n] + c[n], {n, 2, 29}] (* Peter Luschny, Jan 23 2018 *)

PROG

(Sage)

def a(n):

     return (sum(ZZ(n - 2) / i * binomial(2 * i - 2, i - 1) *

         binomial(n - 2, 2 * i - 2)

                 for i in range(1, floor(n / 2) + 1)) +

             sum(binomial(n - 1, k) * binomial(n - 1 - k, k)

                 for k in range(floor((n - 1) / 2) + 1)))

CROSSREFS

Cf. A001006 (type A), A002426 (type B), A290380.

Sequence in context: A165993 A192312 A004080 * A027115 A077995 A276293

Adjacent sequences:  A298297 A298298 A298299 * A298301 A298302 A298303

KEYWORD

nonn

AUTHOR

F. Chapoton, Jan 16 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 16 15:31 EDT 2019. Contains 328101 sequences. (Running on oeis4.)