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

0,5

Comments

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

Links

Table of n, a(n) for n=0..64.

John Tyler Rascoe, Python program

Example

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)

Prog

(Python) # see linked program

Crossrefs

Cf. A016116 (symmetric compositions).

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

Cf. A003242, A350837.

Sequence in context: A269501 A254044 A274515 * A291564 A029266 A325035

Adjacent sequences: A362497 A362498 A362499 * A362501 A362502 A362503

Keyword

nonn

Author

John Tyler Rascoe, Apr 22 2023

Status

approved