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!)
A329058 2-parking triangle T(r, i, 2) read by rows: T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i) with k = 2 and 0 <= i <= r. 5
1, 2, 1, 7, 6, 3, 30, 36, 32, 16, 143, 220, 275, 250, 125, 728, 1365, 2184, 2808, 2592, 1296, 3876, 8568, 16660, 27440, 36015, 33614, 16807, 21318, 54264, 124032, 248064, 417792, 557056, 524288, 262144, 120175, 346104, 908523, 2133054, 4363065, 7479540, 10097379, 9565938, 4782969 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The k-parking numbers interpolate between the generalized Fuss-Catalan numbers and the number of parking functions (see Yip).

LINKS

Stefano Spezia, First 151 rows of the triangle, flattened

Martha Yip, A Fuss-Catalan variation of the caracol flow polytope, arXiv:1910.10060 [math.CO], 2019.

FORMULA

T(r, i, k) = (r + 1)^(i-1)*binomial(k*(r + 1) + r - i - 1, r - i).

T(r, 0, 2) = A006013(r).

T(r, r, 2) = A000272(r + 1).

EXAMPLE

r/i|   0   1   2   3   4

————————————————————————

0  |   1

1  |   2   1

2  |   7   6   3

3  |  30  36  32  16

4  | 143 220 275 250 125

MATHEMATICA

T[r_, i_, k_] := (r + 1)^(i-1)*Binomial[k*(r + 1) + r - i - 1, r - i]; Flatten[Table[T[r, i, 2], {r, 0, 9}, {i, 0, r}]]

CROSSREFS

Cf. A000108, A000272, A006013, A007318, A329057, A329059, A329060, A329113 (row sums).

Sequence in context: A178120 A180568 A248950 * A078301 A160201 A204912

Adjacent sequences:  A329055 A329056 A329057 * A329059 A329060 A329061

KEYWORD

nonn,tabl

AUTHOR

Stefano Spezia, Nov 02 2019

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 June 14 05:10 EDT 2021. Contains 345018 sequences. (Running on oeis4.)