A343578 - OEIS

%I #31 May 02 2021 18:09:47

%S 2,58,178,362,610,922,1298,1738,2242,2810,3442,4138,4898,5722,6610,

%T 7562,8578,9658,10802,12010,13282,14618,16018,17482,19010,20602,22258,

%U 23978,25762,27610,29522,31498,33538,35642,37810,40042,42338,44698,47122,49610,52162,54778,57458

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

%C 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).

%C 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

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: 2*x*(1 + 26*x + 5*x^2)/(1 - x)^3. - _Stefano Spezia_, Apr 22 2021

%F a(n) = 4*A014634(n-1) - 2 = 8*A033954(n-1) + 2. - _Hugo Pfoertner_, Apr 24 2021

%F a(n) = determinant(matrix[4*n-1, -4*n+2, 4*n-3, 4*n-4]). - _Peter Luschny_, Apr 24 2021

%F a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - _Wesley Ivan Hurt_, May 02 2021

%t Table[32*n^2 - 40*n + 10, {n, 50}] (* _Wesley Ivan Hurt_, May 02 2021 *)

%Y Cf. A274979 (generalized 18-gonal numbers).

%K nonn,easy

%O 1,1

%A _Gavin Lupo_, Apr 20 2021