A055659 Number of (2,n)-partitions of a chain of length n^3.

0, 15, 253, 1653, 6786, 21115, 54615, 123753, 253828, 481671, 858705, 1454365, 2359878, 3692403, 5599531, 8264145, 11909640, 16805503, 23273253, 31692741, 42508810, 56238315, 73477503, 94909753, 121313676, 153571575, 192678265, 239750253, 296035278, 362922211, 441951315

Offset

1,2

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

G.f.: x^2*(15 + 148*x + 197*x^2 + 3*x^3 - 4*x^4 + x^5)/(1 - x)^7. - Andrew Howroyd, Oct 24 2025

Example

a(2)=15 because in the linearly ordered set {1,..,8} we can choose in 15 ways 2 successive blocks of 2 consecutive elements.

Prog

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

Crossrefs

Cf. A055658.

Sequence in context: A066410 A370317 A116508 * A218368 A123816 A273921

Adjacent sequences: A055656 A055657 A055658 * A055660 A055661 A055662

Keyword

nonn,easy

Author

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

Status

approved