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

2,1

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).

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)

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 *)

Prog

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

Crossrefs

Sequence in context: A137184 A153244 A200774 * A022276 A171443 A341403

Adjacent sequences: A273217 A273218 A273219 * A273221 A273222 A273223

Keyword

nonn,easy

Author

Dimitri Boscainos, May 18 2016

Status

approved