A063488 a(n) = (2*n-1)*(n^2 -n +2)/2.

1, 6, 20, 49, 99, 176, 286, 435, 629, 874, 1176, 1541, 1975, 2484, 3074, 3751, 4521, 5390, 6364, 7449, 8651, 9976, 11430, 13019, 14749, 16626, 18656, 20845, 23199, 25724, 28426, 31311, 34385, 37654, 41124, 44801, 48691, 52800, 57134, 61699, 66501, 71546, 76840

Offset: 1

Author

N. J. A. Sloane, Aug 01 2001

Keywords

• nonn
• easy

Comments

Sum of two consecutive terms of A006003(n) = n*(n^2+1)/2. a(n) = A006003(n-1) + A006003(n). - Alexander Adamchuk, Jun 03 2006

If a 2-set Y and a 3-set Z are disjoint subsets of an n-set X then a(n-4) is the number of 5-subsets of X intersecting both Y and Z. - Milan Janjic, Sep 08 2007

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000
• Milan Janjic, Two Enumerative Functions
• Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
• T. P. Martin, Shells of atoms, Phys. Rep., 273 (1996), 199-241, eq. (10).
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

1/12*t*n*(2*n^2 - 3*n + 1) + 2*n - 1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.

Cf. A000217, A006003.

Partial sums of A005918.

Programs

Magma

[(2*n-1)*(n^2 -n +2)/2: n in [1..30]]; // G. C. Greubel, Dec 01 2017

Mathematica

Table[(2 n - 1) (n^2 - n + 2)/2, {n, 1, 40}] (* Bruno Berselli, Oct 14 2016 *)
LinearRecurrence[{4,-6,4,-1}, {1,6,20,49}, 50] (* G. C. Greubel, Dec 01 2017 *)

PARI

a(n) = { (2*n - 1)*(n^2 - n + 2)/2 } \\ Harry J. Smith, Aug 23 2009

PARI

my(x='x+O('x^30)); Vec(serlaplace((-2 + 4*x + 3*x^2 + 2*x^3)*exp(x)/2 + 1)) \\ G. C. Greubel, Dec 01 2017

Formula

G.f.: (1 + x)*(1 + x + x^2)/(1 - x)^4. - Jaume Oliver Lafont, Aug 30 2009

a(n) = A000217(A000217(n)) - A000217(A000217(n-2)). - Bruno Berselli, Oct 14 2016

E.g.f.: (-2 + 4*x + 3*x^2 + 2*x^3)*exp(x)/2 + 1. - G. C. Greubel, Dec 01 2017