A034324 a(n) = (n-1)*(n-2)*(n-3) + n.

1, 2, 3, 10, 29, 66, 127, 218, 345, 514, 731, 1002, 1333, 1730, 2199, 2746, 3377, 4098, 4915, 5834, 6861, 8002, 9263, 10650, 12169, 13826, 15627, 17578, 19685, 21954, 24391, 27002, 29793, 32770, 35939, 39306, 42877, 46658, 50655, 54874, 59321

Offset

1,2

Comments

(n*a(n+1)^3+1)/(n^3+1) is the smallest integer of the form (n*k^3+1)/(n^3+1). - Benoit Cloitre, May 02 2002

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Dorin Andrica and Ovidiu Bagdasar, On k-partitions of multisets with equal sums, The Ramanujan J. (2021) Vol. 55, 421-435.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = (n-2)^3 + 2 = A084380(n-2). - Philippe Deléham, Feb 23 2014

a(n+1) = A002061(n)*(n-2) + 3. - Philippe Deléham, Feb 23 2014

G.f.: x*(1-2*x+x^2+6*x^3)/(1-x)^4. - Philippe Deléham, Feb 23 2014

E.g.f.: 6 + (x^3-3*x^2+7*x-6)*exp(x). - Nikolaos Pantelidis, Feb 06 2023

Maple

seq( (n-2)^3 +2, n=1..50); # G. C. Greubel, Aug 23 2019

Mathematica

Table[(n-3)(n-2)(n-1)+n, {n, 50}] (* or *) Table[n^3+2, {n, -1, 50}]  (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)
CoefficientList[Series[(1 -2x +x^2 +6x^3)/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Feb 24 2014 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 2, 3, 10}, 50] (* Harvey P. Dale, Aug 06 2018 *)

Prog

(PARI) a(n)=(n-3)*(n-2)*(n-1)+n \\ Charles R Greathouse IV, Jul 02 2016
(Magma) [(n-2)^3 +2: n in [1..50]]; // G. C. Greubel, Aug 23 2019
(Sage) [(n-2)^3 +2 for n in (1..50)] # G. C. Greubel, Aug 23 2019
(GAP) List([1..50], n-> (n-2)^3 +2); # G. C. Greubel, Aug 23 2019

Crossrefs

Cf. A000578, A084378, A084381.

Sequence in context: A058953 A160909 A004980 * A084380 A363139 A286814

Adjacent sequences: A034321 A034322 A034323 * A034325 A034326 A034327

Keyword

easy,nonn

Author

Laurence Michaels (guardian(AT)ntplx.net)

Extensions

Extended and corrected by Erich Friedman

Status

approved