A100019 a(n) = n^4 + n^3 + n^2.

0, 3, 28, 117, 336, 775, 1548, 2793, 4672, 7371, 11100, 16093, 22608, 30927, 41356, 54225, 69888, 88723, 111132, 137541, 168400, 204183, 245388, 292537, 346176, 406875, 475228, 551853, 637392, 732511, 837900, 954273, 1082368, 1222947

Offset

0,2

Comments

a(n) are the numbers m such that: j^2 = j + m + sqrt(j*m) with corresponding numbers j given by A002061(n+1), and with sqrt(j*m) = A027444(n) = n* A002061(n+1). - Richard R. Forberg, Sep 03 2013.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Formula

From Indranil Ghosh, Apr 15 2017: (Start)

G.f.: -x(3 + 13x + 7x^2 + x^3)/(x - 1)^5

E.g.f.: exp(x)*x*(3 + 11x + 7x^2 + x^3)

(End)

Maple

A100019:=n->n^4+n^3+n^2: seq(A100019(n), n=0..50); # Wesley Ivan Hurt, Apr 14 2017

Mathematica

f[n_]:=n^4+n^3+n^2; Array[f, 50, 0] (* Vladimir Joseph Stephan Orlovsky, Apr 12 2011 *)

Prog

(Magma) [n^4+n^3+n^2: n in [0..50]]; // Vincenzo Librandi, Jun 09 2011
(PARI) a(n) = n^4 + n^3 + n^2 \\ Indranil Ghosh, Apr 15 2017

Crossrefs

Cf. A000583, A002523, A091940, A071253, A059826, A027445, A053699.

Sequence in context: A107651 A239057 A338791 * A053132 A316390 A048367

Adjacent sequences: A100016 A100017 A100018 * A100020 A100021 A100022

Keyword

nonn,easy

Author

Douglas Winston (douglas.winston(AT)srupc.com), Nov 19 2004

Status

approved