cp's OEIS Frontend

A214177 Sum of the 4 nearest neighbors of n in a spiral with positive integers.

%I A214177 #17 Dec 15 2023 14:37:14
%S A214177 20,24,32,24,44,32,56,40,44,72,52,56,88,64,68,72,108,80,84,88,128,96,
%T A214177 100,104,108,152,116,120,124,128,176,136,140,144,148,152,204,160,164,
%U A214177 168,172,176,232,184,188,192,196,200,204,264,212,216,220,224,228,232,296
%N A214177 Sum of the 4 nearest neighbors of n in a spiral with positive integers.
%C A214177 Nearby numbers on diagonals are not counted as neighbors for this sequence.
%H A214177 Rémy Sigrist, <a href="/A214177/b214177.txt">Table of n, a(n) for n = 1..5202</a>
%H A214177 Rémy Sigrist, <a href="/A214177/a214177.gp.txt">PARI program for A214177</a>
%F A214177 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 A214177 Spiral begins:
%e A214177 .
%e A214177   49  26--27--28--29--30--31
%e A214177    |   |                   |
%e A214177   48  25  10--11--12--13  32
%e A214177    |   |   |           |   |
%e A214177   47  24   9   2---3  14  33
%e A214177    |   |   |   |   |   |   |
%e A214177   46  23   8   1   4  15  34
%e A214177    |   |   |       |   |   |
%e A214177   45  22   7---6---5  16  35
%e A214177    |   |               |   |
%e A214177   44  21--20--19--18--17  36
%e A214177    |                       |
%e A214177   43--42--41--40--39--38--37
%e A214177 .
%e A214177 The four nearest neighbors of 2 are 1, 3, 9, 11. Their sum is a(2) = 24.
%o A214177 (PARI) See Links section.
%Y A214177 Cf. A137928, A137930, A137931, A002061, A114254.
%Y A214177 Cf. A214176 (sum of the 8 nearest neighbors).
%K A214177 nonn,easy
%O A214177 1,1
%A A214177 _Alex Ratushnyak_, Jul 06 2012