A139597 A139278(n) followed by A139274(n+1).

0, 7, 15, 30, 46, 69, 93, 124, 156, 195, 235, 282, 330, 385, 441, 504, 568, 639, 711, 790, 870, 957, 1045, 1140, 1236, 1339, 1443, 1554, 1666, 1785, 1905, 2032, 2160, 2295, 2431, 2574, 2718, 2869, 3021, 3180, 3340, 3507, 3675, 3850

Offset

0,2

Comments

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.

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 + 7n, 8*(n+1)^2 - (n+1).

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]

Example

Array begins:
0, 7
15, 30
46, 69
93, 124

Crossrefs

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

Sequence in context: A299509 A299309 A300110 * A210675 A293361 A117747

Adjacent sequences: A139594 A139595 A139596 * A139598 A139599 A139600

Keyword

easy,nonn

Author

Omar E. Pol, May 03 2008

Status

approved