OFFSET
0,3
COMMENTS
Note (in reference to FAMP program code): 1kbasejrokseq = A005286 (Number of permutations of [n+3] with three inversions), 1ibasekrokseq = A004006 = C(n,1) + C(n,2) + C(n,3) (from second term).
Floretion Algebra Multiplication Program, FAMP Code: a(n) = -1tesrok[(- 'j + 'k - 'ii' - 'ij' - 'ik')(- 'i + 'j - 'kk' - 'ki' - 'kj'), Roktype: Y[sqa.Findk()] = Y[sqa.Findk()] + p (internal program code).
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = n*(n+2)*(n+1)/3 - 1 = 2*A000292(n) - 1.
G.f.: (-1 + 5*x - 3*x^2 + x^3)/(x-1)^4.
MAPLE
a[0]:=-1:a[1]:=1:for n from 2 to 50 do a[n]:=a[n-1]+n^2+n od: seq(a[n], n=0..49); .
MATHEMATICA
s1=s2=s3=s4=0; lst={}; Do[a=n+(n+2); s1+=a; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst, s2-1], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 04 2009 *)
2 Binomial[Range[2, 60], 3]-1 (* Harvey P. Dale, Aug 19 2021 *)
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Creighton Dement, Jun 24 2005
STATUS
approved