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

0, 2, 10, 20, 36, 54, 78, 104, 136, 170, 210, 252, 300, 350, 406, 464, 528, 594, 666, 740, 820, 902, 990, 1080, 1176, 1274, 1378, 1484, 1596, 1710, 1830, 1952, 2080, 2210, 2346, 2484, 2628, 2774, 2926, 3080, 3240, 3402, 3570, 3740

Offset

0,2

Comments

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.

a(n) = 2*A006578(n) - A002378(n)/2 = 2*A035608(n). [From Reinhard Zumkeller, Feb 07 2010]

Links

Table of n, a(n) for n=0..43.

Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).

Formula

Array read by rows: row n gives 8*n^2 + 2n, 8*(n+1)^2 - 6(n+1).

a(n) = 2*floor((n + 1/4)^2). [From Reinhard Zumkeller, Feb 07 2010]

G.f.: 2*x*(1+3*x)/((1-x)^3*(1+x)). [Colin Barker, Apr 26 2012]

Example

Array begins:
0, 2
10, 20
36, 54
78, 104

Crossrefs

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

Sequence in context: A305448 A177150 A165551 * A294544 A285104 A332393

Adjacent sequences: A139589 A139590 A139591 * A139593 A139594 A139595

Keyword

easy,nonn

Author

Omar E. Pol, May 03 2008

Status

approved