A085786 a(n) = n*(2*n^2 + n + 1)/2.

2, 11, 33, 74, 140, 237, 371, 548, 774, 1055, 1397, 1806, 2288, 2849, 3495, 4232, 5066, 6003, 7049, 8210, 9492, 10901, 12443, 14124, 15950, 17927, 20061, 22358, 24824, 27465, 30287, 33296, 36498, 39899, 43505, 47322, 51356, 55613, 60099, 64820

Offset: 1

Author

Jon Perry, Jul 23 2003

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000217 [t(n)], A000096 [t(n)+n], A005449 [t(n)+n^2].

a(n) = A110449(n, n).

Programs

Magma

[n*(2*n^2 + n + 1)/2: n in [1..40]]; // Vincenzo Librandi, Aug 14 2017

Mathematica

CoefficientList[Series[(x + 1) (x + 2) / (x - 1)^4, {x, 0, 40}], x] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 11, 33, 74}, 40] (* Vincenzo Librandi, Aug 14 2017 *)

PARI

t(n)=n*(n+1)/2;
vector(40, i, t(i)+i^3)

Formula

a(n) = A000217(n) + n^3.

From Colin Barker, Jan 20 2014: (Start)

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

G.f.: x*(x+1)*(x+2) / (x-1)^4. (End)

E.g.f.: (x/2)*(4 + 7*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 24 2017

Extensions

Name changed by Wesley Ivan Hurt, Apr 30 2022