A055658 Number of (3,n)-partitions of a chain of length n^2.

0, 0, 1, 35, 286, 1330, 4495, 12341, 29260, 62196, 121485, 221815, 383306, 632710, 1004731, 1543465, 2303960, 3353896, 4775385, 6666891, 9145270, 12347930, 16435111, 21592285, 28032676, 35999900, 45770725, 57657951, 72013410

Offset

1,4

Comments

a (k,n)-partition of a chain C is a chain of k intervals of C of length n.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

a(n) = (1/6)*(n-1)*(n-2)*(n^2-3*n+3)*(n^2-3*n+1).

G.f.: -x^3*(1+28*x+62*x^2+28*x^3+x^4) / (x-1)^7. - R. J. Mathar, Mar 14 2016

Example

a(3)=1 because in the linearly ordered set {1,..,9} we can choose in just one way 3 successive blocks of 3 consecutive elements.

Prog

(Magma) [1/6*(n-1)*(n-2)*(n^2-3*n+3)*(n^2-3*n+1): n in [1..35]]; // Vincenzo Librandi, Jun 30 2011
(PARI) a(n) = (n-1)*(n-2)*(n^2-3*n+3)*(n^2-3*n+1)/6; \\ Altug Alkan, Oct 04 2018

Crossrefs

Cf. A055659.

Sequence in context: A210269 A219575 A219711 * A341441 A125773 A198397

Adjacent sequences: A055655 A055656 A055657 * A055659 A055660 A055661

Keyword

nonn,easy

Author

Paolo Dominici (pl.dm(AT)libero.it), Jun 07 2000

Status

approved