A078510 Spiro-Fibonacci numbers, a(n) = sum of two previous terms that are nearest when terms arranged in a spiral.

0, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 21, 24, 27, 31, 36, 42, 48, 54, 61, 69, 78, 88, 98, 108, 119, 131, 144, 158, 172, 186, 201, 217, 235, 256, 280, 304, 328, 355, 386, 422, 464, 512, 560, 608, 662, 723, 792, 870, 958, 1056

Offset: 0

Author

Neil Fernandez, Jan 05 2003

Keywords

• nonn

Comments

Or "Spironacci numbers" for short. See also Spironacci polynomials, A265408. This sequence has an interesting growth rate, see A265370 and A265404. - Antti Karttunen, Dec 13 2015

Examples

			Terms are written in square boxes radiating spirally (cf. Ulam prime spiral). a(0)=0 and a(1)=1, so write 0 and then 1 to its right. a(2) goes in the box below a(1). The nearest two filled boxes contain a(0) and a(1), so a(2)=a(0)+a(1)=0+1=1. a(3) goes in the box to the left of a(2). The nearest two filled boxes contain a(0) and a(2), so a(3)=a(0)+a(2)=0+1=1.
From _Antti Karttunen_, Dec 17 2015: (Start)
The above description places cells in clockwise direction. However, for the computation of this sequence the actual orientation of the spiral is irrelevant. Following the convention used at A265409, we draw this spiral counterclockwise:
+--------+--------+--------+--------+
|a(15)   |a(14)   |a(13)   |a(12)   |
| = a(14)| = a(13)| = a(12)| = a(11)|
| + a(4) | + a(3) | + a(2) | + a(2) |
| = 9    | = 8    | = 7    | = 6    |
+--------+--------+--------+--------+
|a(4)    |a(3)    |a(2)    |a(11)   |
| = a(3) | = a(2) | = a(1) | = a(10)|
| + a(0) | + a(0) | + a(0) | + a(2) |
| = 1    | = 1    | = 1    | = 5    |
+--------+--------+--------+--------+
|a(5)    | START  |   ^    |a(10)   |
| = a(4) | a(0)=0 | a(1)=1 | = a(9) |
| + a(0) |   -->  |        | + a(1) |
| = 1    |        |        | = 4    |
+--------+--------+--------+--------+
|a(6)    |a(7)    |a(8)    |a(9)    |
| = a(5) | = a(6) | = a(7) | = a(8) |
| + a(0) | + a(0) | + a(1) | + a(1) |
| = 1    | = 1    | = 2    | = 3    |
+--------+--------+--------+--------+
(End)
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..1024

Crossrefs

Cf. A000045, A001222, A033951, A063826, A265407, A265408, A265409, A265359, A265370, A265404.

Formula

From Antti Karttunen, Dec 13 2015: (Start)

a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) + a(A265409(n)).

equally, for n > 1, a(n) = a(n-1) + a(n - A265359(n)).

a(n) = A001222(A265408(n)).

(End)