A160805 a(n) = (2*n^3 + 9*n^2 + n + 24) / 6.

4, 6, 13, 27, 50, 84, 131, 193, 272, 370, 489, 631, 798, 992, 1215, 1469, 1756, 2078, 2437, 2835, 3274, 3756, 4283, 4857, 5480, 6154, 6881, 7663, 8502, 9400, 10359, 11381, 12468, 13622, 14845, 16139, 17506, 18948, 20467, 22065, 23744, 25506, 27353, 29287

Offset: 0

Author

Reinhard Zumkeller, May 26 2009

Keywords

• nonn
• easy

Comments

Arithmetic progression of third order; a(n+1)-a(n) = A008865(n+2);

a(n) = A101986(n) + 4.

References

• R. Courant, Differential and Integral Calculus Vol. I (Blackie&Son, 1937), ch. I.4, Example 5, p.29.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

Cf. A008865, A101986.

Programs

Magma

[(2*n^3+9*n^2+n+24)/6: n in [0..50]]; // Vincenzo Librandi, Dec 27 2010

Maple

A160805:=n->(2*n^3+9*n^2+n+24)/6: seq(A160805(n), n=0..80); # Wesley Ivan Hurt, Aug 29 2015

Mathematica

Table[(2 n^3 + 9 n^2 + n + 24)/6, {n, 0, 60}]
CoefficientList[Series[(4 - 10*x + 13*x^2 - 5*x^3)/(x - 1)^4, {x, 0, 60}], x] (* Wesley Ivan Hurt, Aug 29 2015 *)

PARI

first(m)=vector(m,i,i--;(2*i^3 + 9*i^2 + i + 24) / 6) \\ Anders Hellström, Aug 29 2015

Formula

a(n) = (2*n^3 + 9*n^2 + n + 24) / 6.

From Wesley Ivan Hurt, Aug 29 2015: (Start)

G.f.: (4-10*x+13*x^2-5*x^3)/(x-1)^4.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4), n>3. (End)