A017378 a(n) = (10*n + 9)^2.

81, 361, 841, 1521, 2401, 3481, 4761, 6241, 7921, 9801, 11881, 14161, 16641, 19321, 22201, 25281, 28561, 32041, 35721, 39601, 43681, 47961, 52441, 57121, 62001, 67081, 72361, 77841, 83521, 89401, 95481, 101761, 108241, 114921, 121801, 128881, 136161, 143641

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

From Colin Barker, Mar 30 2017: (Start)

G.f.: (81 + 118*x + x^2) / (1 - x)^3.

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

(End)

Maple

A017378:=n->(10*n+9)^2: seq(A017378(n), n=0..50); # Wesley Ivan Hurt, Mar 30 2017

Mathematica

Table[(10 n + 9)^2, {n, 0, 37}] (* or *)
LinearRecurrence[{3, -3, 1}, {81, 361, 841}, 38] (* or *)
CoefficientList[Series[(81 + 118 x + x^2)/(1 - x)^3, {x, 0, 37}], x] (* Michael De Vlieger, Mar 30 2017 *)

Prog

(Magma) [(10*n+9)^2: n in [0..40]]; // Vincenzo Librandi, Aug 31 2011
(PARI) a(n) = (10*n+9)^2; \\ Michel Marcus, Aug 26 2015
(PARI) Vec((81 + 118*x + x^2) / (1 - x)^3 + O(x^40)) \\ Colin Barker, Mar 30 2017

Crossrefs

Cf. A017377.

Sequence in context: A236990 A236058 A205513 * A205736 A237850 A205917

Adjacent sequences: A017375 A017376 A017377 * A017379 A017380 A017381

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved