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

1,1

Comments

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

Links

Rémy Sigrist, Table of n, a(n) for n = 1..5202

Rémy Sigrist, PARI program for A214177

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

Example

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.

Prog

(PARI) See Links section.

Crossrefs

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

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

Sequence in context: A109131 A171696 A060461 * A044996 A347190 A263016

Adjacent sequences: A214174 A214175 A214176 * A214178 A214179 A214180

Keyword

nonn,easy

Author

Alex Ratushnyak, Jul 06 2012

Status

approved