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A273220
a(n) = 8n^2 - 12n + 1.
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
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
KEYWORD
nonn,easy
AUTHOR
Dimitri Boscainos, May 18 2016
STATUS
approved