A395554 - OEIS

A395554

Number of no-overhang stacked partitions (teeth) of base 5 and total size n.

1, 5, 9, 16, 28, 45, 68, 98, 137, 188, 251, 328, 421, 534, 667, 823, 1006, 1217, 1459, 1736, 2050, 2406, 2805, 3251, 3749, 4303, 4915, 5589, 6331, 7145, 8034, 9004, 10058, 11203, 12443, 13782, 15227, 16783, 18454, 20247, 22168, 24223, 26416, 28755, 31246, 33896

(list; graph; refs; listen; history; text; internal format)

OFFSET

5,2

COMMENTS

A tooth of base r is a finite stack of rows of unit cubes with bottom row of length r, weakly decreasing row lengths, and no row overhanging the row beneath it. This sequence is column c=5 of the triangle A072704.

REFERENCES

Paul M. King, Generating Functions for Temperley's No-Overhang Stacked Partitions, Journal of Integer Sequences (submitted).

LINKS

Table of n, a(n) for n=5..50.

Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,-1,-1,1,1,1,0,0,-1,-1,1).

FORMULA

G.f.: h_5(q) = q^5*(1+q)*(1+4q+3q^2+2q^3+3q^4+q^5+q^6)/((1-q)*(1-q^2)*(1-q^3)*(1-q^4)*(1-q^5)).

T(5,N) = [q^N] h_5(q) where h_r(q) satisfies (1-q^r)*h_r(q) = 2q*h_{r-1}(q) - q^2*h_{r-2}(q), with h_0(q)=1 and h_1(q)=q/(1-q).

CROSSREFS

Column 5 of A072704.

Cf. A000012 (c=1), A001477 (c=2), A000212 (c=3, with offset), A395553 (c=4).

Sequence in context: A233184 A356675 A072174 * A188555 A020958 A020750

Adjacent sequences: A395550 A395551 A395553 * A395558 A395559 A395560

KEYWORD

nonn,easy,new

AUTHOR

Paul M. King, Apr 28 2026

STATUS

approved