A139591 - OEIS

%I #17 Jul 14 2022 17:24:26

%S 0,1,9,18,34,51,75,100,132,165,205,246,294,343,399,456,520,585,657,

%T 730,810,891,979,1068,1164,1261,1365,1470,1582,1695,1815,1936,2064,

%U 2193,2329,2466,2610,2755,2907,3060,3220,3381,3549,3718,3894,4071,4255,4440,4632

%N A139275(n) followed by 18-gonal number A051870(n+1).

%C Sequence found by reading the line from 0, in the direction 0, 9, ... and the line from 1, in the direction 1, 18, ..., in the square spiral whose vertices are the triangular numbers A000217.

%H Omar E. Pol, <a href="http://www.polprimos.com">Determinacion geometrica de los numeros primos y perfectos</a>.

%F Array read by rows: row n gives 8*n^2 + n, 8*(n+1)^2 - 7*(n+1).

%F G.f.: -x*(7*x+1)/((x-1)^3*(x+1)). - _Colin Barker_, Oct 16 2012

%F a(n) = 2*n^2 + (7/2)*n + (3/4)*((-1)^n-1). - _Sean A. Irvine_, Jul 14 2022

%e Array begins:

%e    0,   1;

%e    9,  18;

%e   34,  51;

%e   75, 100;

%e   ...

%Y Cf. A000217, A046092, A051870, A139275, A077221, A139592, A139593, A139595, A139596, A139597, A139598.

%Y Partial sums of A047393.

%K nonn,easy,tabf

%O 0,3

%A _Omar E. Pol_, May 03 2008