A139591 A139275(n) followed by 18-gonal number A051870(n+1).

0, 1, 9, 18, 34, 51, 75, 100, 132, 165, 205, 246, 294, 343, 399, 456, 520, 585, 657, 730, 810, 891, 979, 1068, 1164, 1261, 1365, 1470, 1582, 1695, 1815, 1936, 2064, 2193, 2329, 2466, 2610, 2755, 2907, 3060, 3220, 3381, 3549, 3718, 3894, 4071, 4255, 4440, 4632

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..48.

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

Formula

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

G.f.: -x*(7*x+1)/((x-1)^3*(x+1)). - Colin Barker, Oct 16 2012

a(n) = 2*n^2 + (7/2)*n + (3/4)*((-1)^n-1). - Sean A. Irvine, Jul 14 2022

Example

Array begins:
   0,   1;
   9,  18;
  34,  51;
  75, 100;
  ...

Crossrefs

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

Partial sums of A047393.

Sequence in context: A183444 A349417 A221533 * A191268 A109668 A234598

Adjacent sequences: A139588 A139589 A139590 * A139592 A139593 A139594

Keyword

nonn,easy,tabf

Author

Omar E. Pol, May 03 2008

Status

approved