OFFSET
0,2
COMMENTS
Fourth column (m=3) of triangle A060098.
Partial sums of A038163.
Equals the tetrahedral numbers, [1, 4, 10, 20, ...] convolved with the aerated triangular numbers, [1, 0, 3, 0, 6, 0, 10, ...]. [Gary W. Adamson, Jun 11 2009]
REFERENCES
B. Broer, Hilbert series for modules of covariants, in Algebraic Groups and Their Generalizations..., Proc. Sympos. Pure Math., 56 (1994), Part I, 321-331. See p. 329.
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 0..9999
Jia Huang, Partially Palindromic Compositions, J. Int. Seq. (2023) Vol. 26, Art. 23.4.1. See pp. 4, 20.
Index entries for linear recurrences with constant coefficients, signature (4,-3,-8,14,0,-14,8,3,-4,1).
FORMULA
a(n) = Sum_{} A060098(n+3, 3).
G.f.: 1/((1-x)^7*(1+x)^3).
MATHEMATICA
a[n_]:=If[OddQ[n], ((1+n) (3+n) (5+n)^2 (7+n) (9+n))/5760, ((2+n) (4+n) (6+n) (8+n) (15+10 n+n^2))/5760]; Map[a, Range[0, 100]] (* Peter J. C. Moses, Mar 24 2013 *)
CoefficientList[Series[1/((1-x^2)^3*(1-x)^4), {x, 0, 100}], x] (* Peter J. C. Moses, Mar 24 2013 *)
LinearRecurrence[{4, -3, -8, 14, 0, -14, 8, 3, -4, 1}, {1, 4, 13, 32, 71, 140, 259, 448, 742, 1176}, 40] (* Harvey P. Dale, Apr 06 2018 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, Apr 06 2001
STATUS
approved