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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A275207 Expansion of (A(x)^2+A(x^2))/2 where A(x) = A001006(x). 2
1, 1, 3, 6, 16, 38, 100, 256, 681, 1805, 4867, 13162, 35925, 98469, 271511, 751656, 2089963, 5831451, 16326785, 45847770, 129108926, 364498596, 1031486590, 2925337352, 8313215743, 23668977163, 67507773621, 192859753310, 551821400008, 1581188102590 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Analog of A275165 with Motzkin numbers replacing connected graph counts.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(2n+1) = A275208(2n+1).

Conjecture: a(2n+1) = A026940(n+1).

MAPLE

b:= proc(n) option remember; `if`(n<2, 1,

      ((3*(n-1))*b(n-2)+(1+2*n)*b(n-1))/(n+2))

    end:

a:= proc(n) option remember; add(b(j)*b(n-j), j=0..n/2)-

      `if`(n::odd, 0, (t-> t*(t-1)/2)(b(n/2)))

    end:

seq(a(n), n=0..40);  # Alois P. Heinz, Jul 19 2016

MATHEMATICA

b[n_] := b[n] = If[n<2, 1, ((3*(n-1))*b[n-2] + (1+2*n)*b[n-1])/(n+2)];

a[n_] := a[n] = Sum[b[j]*b[n-j], {j, 0, n/2}] - If[OddQ[n], 0, Function[t, t*(t-1)/2][b[n/2]]];

Table[a[n], {n, 0, 40}] (* Jean-Fran├žois Alcover, May 16 2017, after Alois P. Heinz *)

CROSSREFS

Cf. A275208, A026940.

Sequence in context: A190735 A096588 A256943 * A073079 A143560 A279685

Adjacent sequences:  A275204 A275205 A275206 * A275208 A275209 A275210

KEYWORD

nonn

AUTHOR

R. J. Mathar, Jul 19 2016

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 June 25 18:38 EDT 2022. Contains 354851 sequences. (Running on oeis4.)