A169938 a(n) = n*(n+1)*(n*(n+1)+1).

0, 0, 6, 42, 156, 420, 930, 1806, 3192, 5256, 8190, 12210, 17556, 24492, 33306, 44310, 57840, 74256, 93942, 117306, 144780, 176820, 213906, 256542, 305256, 360600, 423150, 493506, 572292, 660156, 757770, 865830, 985056, 1116192, 1260006, 1417290, 1588860

Offset

-1,3

Comments

Partial sums of A061804. - Bruno Berselli, Feb 10 2017

Links

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

Nathan Kaplan, Susie Kimport, Rachel Lawrence, Luke Peilen, and Max Weinreich, Counting arcs in projective planes via Glynn’s algorithm, J. Geom. 108, No. 3 (2017), 1013-1029, Th. 1.4, C_2.

Daniel Poveda Parrilla, Illustration of initial terms seen as cuboids.

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n+1) = a(n) + 2*(n+1)*(2*(n+1)^2+1). - Robert Munafo, Jul 27 2010

G.f.: 6*x*(1 + 2*x + x^2)/(1-x)^5. - Vincenzo Librandi, Dec 18 2012, corrected Aug 29 2022

From Daniel Poveda Parrilla, Jun 08 2017 and Jun 11 2017: (Start)

a(n) = A002378(n)*A002061(n+1) for n > -1.

a(n) = A002061(A002061(n+1)) - 1. (End)

a(n) = 5*a(n-1)-10*a(n-2)+10*a(n-3)-5*a(n-4)+a(n-5). - Wesley Ivan Hurt, Jan 25 2022

a(n) = 6*A006325(n+1). - R. J. Mathar, Aug 29 2022

Sum_{n>=1} 1/a(n) = 2 - tanh(sqrt(3)*Pi/2)*Pi/sqrt(3). - Amiram Eldar, Sep 22 2022

Maple

A169938 := proc(n)
    n*(n+1)*(n*(n+1)+1);
end proc:
seq(A169938(n), n=-1..40) ; # R. J. Mathar, Aug 29 2022

Mathematica

CoefficientList[Series[6*x^2(1 + 2*x + x^2)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2012 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 0, 6, 42, 156}, 40] (* Harvey P. Dale, Oct 14 2023 *)

Prog

(Magma) [n*(n+1)*(n*(n+1)+1): n in [-1..40]]; // Vincenzo Librandi, Dec 18 2012
(PARI) a(n) = n + 2*n^2 + 2*n^3 + n^4; \\ Altug Alkan, Feb 10 2017
(PARI) a(n) = n*=n+1; n*=n+1 \\ David A. Corneth, Jun 11 2017
(Python)
def A169938(n): return n*(n*(n*(n + 2) + 2) + 1) # Chai Wah Wu, Aug 29 2022

Crossrefs

A variant of A176780.

Cf. A002061, A002378, A061804.

A lower bound on A082986.

Sequence in context: A199905 A360757 A176780 * A082986 A180806 A253946

Adjacent sequences: A169935 A169936 A169937 * A169939 A169940 A169941

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 25 2010, based on an email from Terry Stickel

Extensions

The terms were also computed by Robert Munafo, Jul 25 2010

Status

approved