A301502 Number of compositions (ordered partitions) of n into triangular parts (A000217) such that no two adjacent parts are equal (Carlitz compositions).

1, 1, 0, 1, 2, 1, 1, 3, 3, 3, 7, 9, 6, 10, 20, 20, 20, 36, 50, 54, 75, 109, 126, 156, 233, 302, 352, 480, 676, 838, 1053, 1447, 1896, 2374, 3152, 4225, 5368, 6923, 9297, 12133, 15472, 20353, 26959, 34779, 45092, 59551, 77717, 100475, 131714, 172949, 224316, 291987, 383418

Offset

0,5

Links

Table of n, a(n) for n=0..52.

Index entries for sequences related to compositions

Index to sequences related to polygonal numbers

Formula

G.f.: 1/(1 - Sum_{k>=1} x^(k*(k+1)/2)/(1 + x^(k*(k+1)/2))).

Example

a(12) = 6 because we have [3, 6, 3], [3, 1, 3, 1, 3, 1], [1, 10, 1], [1, 6, 1, 3, 1], [1, 3, 1, 6, 1] and [1, 3, 1, 3, 1, 3].

Mathematica

nmax = 52; CoefficientList[Series[1/(1 - Sum[x^(k (k + 1)/2)/(1 + x^(k (k + 1)/2)), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Cf. A000217, A003242, A023361, A301503.

Sequence in context: A284828 A101417 A318660 * A260056 A269699 A035636

Adjacent sequences: A301499 A301500 A301501 * A301503 A301504 A301505

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 22 2018

Status

approved