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A139592 A033585(n) followed by A139271(n+1). 9

%I

%S 0,2,10,20,36,54,78,104,136,170,210,252,300,350,406,464,528,594,666,

%T 740,820,902,990,1080,1176,1274,1378,1484,1596,1710,1830,1952,2080,

%U 2210,2346,2484,2628,2774,2926,3080,3240,3402,3570,3740

%N A033585(n) followed by A139271(n+1).

%C Sequence found by reading the line from 0, in the direction 0, 2,... and the same line from 0, in the direction 0, 10,..., in the square spiral whose vertices are the triangular numbers A000217.

%C a(n) = 2*A006578(n) - A002378(n)/2 = 2*A035608(n). [From _Reinhard Zumkeller_, Feb 07 2010]

%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 + 2n, 8*(n+1)^2 - 6(n+1).

%F a(n) = 2*floor((n + 1/4)^2). [From _Reinhard Zumkeller_, Feb 07 2010]

%F G.f.: 2*x*(1+3*x)/((1-x)^3*(1+x)). [_Colin Barker_, Apr 26 2012]

%e Array begins:

%e 0, 2

%e 10, 20

%e 36, 54

%e 78, 104

%Y Cf. A000217, A033585, A046092, A139271, A077221, A139591, A139593, A139595, A139596, A139597, A139598.

%K easy,nonn

%O 0,2

%A _Omar E. Pol_, May 03 2008

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Last modified January 22 13:41 EST 2020. Contains 331149 sequences. (Running on oeis4.)