A273220 a(n) = 8n^2 - 12n + 1.

9, 37, 81, 141, 217, 309, 417, 541, 681, 837, 1009, 1197, 1401, 1621, 1857, 2109, 2377, 2661, 2961, 3277, 3609, 3957, 4321, 4701, 5097, 5509, 5937, 6381, 6841, 7317, 7809, 8317, 8841, 9381, 9937, 10509, 11097, 11701, 12321, 12957, 13609, 14277, 14961, 15661

Offset: 2

Author

Dimitri Boscainos, May 18 2016

Keywords

• nonn
• easy

Comments

Sequence may be obtained by starting with the segment (9, 37) followed by the line from 37 in the direction 37, 81,... in the square spiral whose vertices are the generalized hexagonal numbers (A000217). - Omar E. Pol, Jun 26 2016

Links

• Colin Barker, Table of n, a(n) for n = 2..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Programs

Mathematica

Table[8 n^2 - 12 n + 1, {n, 2, 45}] (* or *)
Drop[#, 2] &@ CoefficientList[Series[x^2 (9 + 10 x - 3 x^2)/(1 - x)^3, {x, 0, 45}], x] (* Michael De Vlieger, Jun 26 2016 *)

PARI

Vec(x^2*(9+10*x-3*x^2)/(1-x)^3 + O(x^50)) \\ Colin Barker, May 18 2016

Formula

From Colin Barker, May 18 2016: (Start)

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>4.

G.f.: x^2*(9+10*x-3*x^2) / (1-x)^3.

(End)