A193608 The consecutive squares of numbers multiplied by their next consecutive integer.

15, 52, 125, 246, 427, 680, 1017, 1450, 1991, 2652, 3445, 4382, 5475, 6736, 8177, 9810, 11647, 13700, 15981, 18502, 21275, 24312, 27625, 31226, 35127, 39340, 43877, 48750, 53971, 59552, 65505, 71842, 78575, 85716, 93277, 101270, 109707, 118600

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

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

Formula

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

G.f.: x*(3-x)*(5-x+2*x^2)/(1-x)^4. [Colin Barker, Mar 28 2012]

Mathematica

Table[2*(n + 1)^3 - n, {n, 38}] (* L. Edson Jeffery, Jan 11 2018 *)
LinearRecurrence[{4, -6, 4, -1}, {15, 52, 125, 246}, 40] (* Harvey P. Dale, May 01 2022 *)

Prog

(C)
int a(int n)
{
    return ((n+2)*((n*n)*((n+1)*(n+1))));
}
(PARI) a(n)=2*n^3+6*n^2+5*n+2 \\ Charles R Greathouse IV, Jul 31 2011
(Magma) [(n+2)*(n^2 + (n+1)^2): n in [1..40] ]; // Vincenzo Librandi, Aug 01 2011

Crossrefs

Sequence in context: A015234 A295339 A346824 * A346857 A332394 A220156

Adjacent sequences: A193605 A193606 A193607 * A193609 A193610 A193611

Keyword

nonn,easy

Author

Ankur Trapasiya, Jul 31 2011

Status

approved