A214177 - OEIS

%I #17 Dec 15 2023 14:37:14

%S 20,24,32,24,44,32,56,40,44,72,52,56,88,64,68,72,108,80,84,88,128,96,

%T 100,104,108,152,116,120,124,128,176,136,140,144,148,152,204,160,164,

%U 168,172,176,232,184,188,192,196,200,204,264,212,216,220,224,228,232,296

%N Sum of the 4 nearest neighbors of n in a spiral with positive integers.

%C Nearby numbers on diagonals are not counted as neighbors for this sequence.

%H Rémy Sigrist, <a href="/A214177/b214177.txt">Table of n, a(n) for n = 1..5202</a>

%H Rémy Sigrist, <a href="/A214177/a214177.gp.txt">PARI program for A214177</a>

%F For n >= 3, a(n+1) - a(n) = 4 except if n = k^2/4 + 3*k/2 + (17 - (-1)^k)/8 for some k >= 1 then a(n+1) - a(n) = 4*k + 16 and if n = k^2/4 + 3*k/2 + (25 - (-1)^k)/8 for some k >= 0 then a(n+1) - a(n) = -4*k - 8. - _Robert Israel_, Dec 14 2023

%e Spiral begins:

%e .

%e   49  26--27--28--29--30--31

%e    |   |                   |

%e   48  25  10--11--12--13  32

%e    |   |   |           |   |

%e   47  24   9   2---3  14  33

%e    |   |   |   |   |   |   |

%e   46  23   8   1   4  15  34

%e    |   |   |       |   |   |

%e   45  22   7---6---5  16  35

%e    |   |               |   |

%e   44  21--20--19--18--17  36

%e    |                       |

%e   43--42--41--40--39--38--37

%e .

%e The four nearest neighbors of 2 are 1, 3, 9, 11. Their sum is a(2) = 24.

%o (PARI) See Links section.

%Y Cf. A137928, A137930, A137931, A002061, A114254.

%Y Cf. A214176 (sum of the 8 nearest neighbors).

%K nonn,easy

%O 1,1

%A _Alex Ratushnyak_, Jul 06 2012