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A139278(n) followed by A139274(n+1).
6

%I #11 Jun 17 2017 04:00:46

%S 0,7,15,30,46,69,93,124,156,195,235,282,330,385,441,504,568,639,711,

%T 790,870,957,1045,1140,1236,1339,1443,1554,1666,1785,1905,2032,2160,

%U 2295,2431,2574,2718,2869,3021,3180,3340,3507,3675,3850

%N A139278(n) followed by A139274(n+1).

%C Sequence found by reading the line from 0, in the direction 0, 7,... and the line from 15, in the direction 15, 46,..., 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>.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,1).

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

%F a(n) = (3-3*(-1)^n+14*n+8*n^2)/4. a(n) = 2*a(n-1)-2*a(n-3)+a(n-4). G.f.: x*(7+x)/((1-x)^3*(1+x)). [_Colin Barker_, Jul 22 2012]

%e Array begins:

%e 0, 7

%e 15, 30

%e 46, 69

%e 93, 124

%Y Cf. A000217, A046092, A139274, A139278, A077221, A139591, A139592, A139593, A139595, A139596, A139598.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, May 03 2008