login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A191397 Triangle read by rows: T(n,k) is the number of dispersed Dyck paths of length n (i.e., Motzkin paths of length n with no (1,0)-steps at positive heights) having k DHU's (here U=(1,1), H=(1,0), and D=(1,-1)). 2
1, 1, 2, 3, 6, 9, 1, 18, 2, 28, 7, 56, 14, 89, 37, 179, 72, 1, 289, 170, 3, 585, 326, 13, 956, 726, 34, 1948, 1380, 104, 3214, 2970, 250, 1, 6591, 5616, 659, 4, 10959, 11829, 1502, 20, 22609, 22300, 3647, 64, 37833, 46306, 8019, 220, 78486, 87154, 18495, 620, 1, 132037, 179222, 39648, 1804, 5 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Row n has 1+floor(n/5) entries.

Sum of entries in row n is binomial(n, floor(n/2)) = A001405(n).

T(n,0) = A191398(n).

Sum_{k>=0} k*T(n,k) = A191389(n-1).

LINKS

Table of n, a(n) for n=0..59.

FORMULA

G.f.: G(t,z) = 2/(1-z-2*z^3-t*z+2*t*z^3+(1-z+t*z)*sqrt(1-4*z^2)).

EXAMPLE

T(6,1)=2 because we have HU(DHU)D and U(DHU)DH, where U=(1,1), D=(1,-1), H=(1,0) (the DHU's are shown between parentheses).

Triangle starts:

   1;

   1;

   2;

   3;

   6;

   9,  1;

  18,  2;

  28,  7;

  56, 14;

MAPLE

G := 2/(1-z-2*z^3-t*z+2*t*z^3+(1-z+t*z)*sqrt(1-4*z^2)): Gser := simplify(series(G, z = 0, 25)): for n from 0 to 21 do P[n] := sort(coeff(Gser, z, n)) end do: for n from 0 to 21 do seq(coeff(P[n], t, k), k = 0 .. floor((1/5)*n)) end do; # yields sequence in triangular form

CROSSREFS

Cf. A001405, A191389, A191398.

Sequence in context: A199790 A088329 A193079 * A087494 A328843 A021426

Adjacent sequences:  A191394 A191395 A191396 * A191398 A191399 A191400

KEYWORD

nonn,tabf

AUTHOR

Emeric Deutsch, Jun 04 2011

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 January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)