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

20, 24, 32, 24, 44, 32, 56, 40, 44, 72, 52, 56, 88, 64, 68, 72, 108, 80, 84, 88, 128, 96, 100, 104, 108, 152, 116, 120, 124, 128, 176, 136, 140, 144, 148, 152, 204, 160, 164, 168, 172, 176, 232, 184, 188, 192, 196, 200, 204, 264, 212, 216, 220, 224, 228, 232, 296

Offset: 1

Author

Alex Ratushnyak, Jul 06 2012

Keywords

• nonn
• easy

Comments

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

Examples

			Spiral begins:
.
  49  26--27--28--29--30--31
   |   |                   |
  48  25  10--11--12--13  32
   |   |   |           |   |
  47  24   9   2---3  14  33
   |   |   |   |   |   |   |
  46  23   8   1   4  15  34
   |   |   |       |   |   |
  45  22   7---6---5  16  35
   |   |               |   |
  44  21--20--19--18--17  36
   |                       |
  43--42--41--40--39--38--37
.
The four nearest neighbors of 2 are 1, 3, 9, 11. Their sum is a(2) = 24.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..5202
• Rémy Sigrist, PARI program for A214177

Crossrefs

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

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

Programs

PARI

See Links section.

Formula

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