A108766 a(n) = A007290(n+2) - 1 = 2*C(n+2,3) - 1.

-1, 1, 7, 19, 39, 69, 111, 167, 239, 329, 439, 571, 727, 909, 1119, 1359, 1631, 1937, 2279, 2659, 3079, 3541, 4047, 4599, 5199, 5849, 6551, 7307, 8119, 8989, 9919, 10911, 11967, 13089, 14279, 15539, 16871, 18277, 19759, 21319, 22959, 24681, 26487, 28379, 30359, 32429, 34591, 36847, 39199, 41649

Offset: 0

Author

Creighton Dement, Jun 24 2005

Keywords

• easy
• sign

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

Crossrefs

Cf. A000292, A007290, A005286, A004006.

Programs

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 *)

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.