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A169938 a(n) = n*(n+1)*(n*(n+1)+1). 4
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 (list; graph; refs; listen; history; text; internal format)
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

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^2(1 + 2*x + x^2)/(1-x)^5. - Vincenzo Librandi, Dec 18 2012

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)

MATHEMATICA

CoefficientList[Series[6*x^2(1 + 2*x + x^2)/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Dec 18 2012 *)

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

CROSSREFS

A variant of A176780.

Cf. A002061, A002378, A061804.

A lower bound on A082986.

Sequence in context: A046763 A199905 A176780 * A082986 A180806 A253946

Adjacent sequences:  A169935 A169936 A169937 * A169939 A169940 A169941

KEYWORD

nonn,easy,changed

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

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Last modified June 26 04:39 EDT 2017. Contains 288752 sequences.