A343578 a(n) = 32*n^2 - 40*n + 10.

2, 58, 178, 362, 610, 922, 1298, 1738, 2242, 2810, 3442, 4138, 4898, 5722, 6610, 7562, 8578, 9658, 10802, 12010, 13282, 14618, 16018, 17482, 19010, 20602, 22258, 23978, 25762, 27610, 29522, 31498, 33538, 35642, 37810, 40042, 42338, 44698, 47122, 49610, 52162, 54778, 57458

Offset: 1

Author

Gavin Lupo, Apr 20 2021

Keywords

• nonn
• easy

Comments

a(n) is the sum of cross multiplying integers in groups of 4, a(n) = (4n-4)*(4n-1) + (4n-3)*(4n-2). For example, the group 4,5,6,7 yields the sum 4*7 + 5*6 = 58 = a(2).

Sequence found by reading the line from 2, in the direction 2, 58, ..., in the square spiral whose vertices are the generalized 18-gonal numbers A274979. - Omar E. Pol, Apr 20 2021

Links

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

Crossrefs

Cf. A274979 (generalized 18-gonal numbers).

Programs

Mathematica

Table[32*n^2 - 40*n + 10, {n, 50}] (* Wesley Ivan Hurt, May 02 2021 *)

Formula

G.f.: 2*x*(1 + 26*x + 5*x^2)/(1 - x)^3. - Stefano Spezia, Apr 22 2021

a(n) = 4*A014634(n-1) - 2 = 8*A033954(n-1) + 2. - Hugo Pfoertner, Apr 24 2021

a(n) = determinant(matrix[4*n-1, -4*n+2, 4*n-3, 4*n-4]). - Peter Luschny, Apr 24 2021

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Wesley Ivan Hurt, May 02 2021