A362500 Number of symmetric compositions of n where differences between adjacent parts are in {-1,1}.

1, 1, 1, 1, 2, 2, 1, 3, 3, 2, 3, 4, 2, 5, 6, 3, 5, 7, 5, 8, 8, 8, 8, 12, 10, 12, 14, 15, 16, 21, 17, 23, 24, 27, 28, 37, 34, 43, 43, 51, 51, 66, 63, 80, 78, 97, 97, 122, 116, 150, 146, 183, 179, 229, 220, 277, 276, 344, 337, 430, 413, 528, 516, 652, 635

Offset: 0

Author

John Tyler Rascoe, Apr 22 2023

Keywords

• nonn

Comments

a(n) and A173258(n) have the same parity.

Examples

			The a(9) = 2 through a(14) = 6 compositions:
  (9)      (10)       (11)       (12)     (13)         (14)
  (12321)  (343)      (434)      (23232)  (454)        (545)
           (1212121)  (32123)             (32323)      (23432)
                      (2121212)           (2123212)    (1232321)
                                          (121212121)  (3212123)
                                                       (212121212)
		

Links

• John Tyler Rascoe, Python program

Crossrefs

Cf. A016116 (symmetric compositions).

Cf. A173258 (compositions where differences between adjacent parts are in {-1,1}).

Cf. A003242, A350837.

Programs

Python

# see linked program