A121832 Expansion of 1/(1-x-x^5-x^6).

1, 1, 1, 1, 1, 2, 4, 6, 8, 10, 13, 19, 29, 43, 61, 84, 116, 164, 236, 340, 485, 685, 965, 1365, 1941, 2766, 3936, 5586, 7916, 11222, 15929, 22631, 32153, 45655, 64793, 91944, 130504, 185288, 263096, 373544, 530281, 752729, 1068521, 1516905

Offset: 0

Author

Jon E. Schoenfield, Aug 27 2006

Keywords

• easy
• nonn

Comments

Number of compositions of n into parts 1, 5, and 6. [Joerg Arndt, Sep 03 2013]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Michael A. Allen, Connections between Combinations Without Specified Separations and Strongly Restricted Permutations, Compositions, and Bit Strings, arXiv:2409.00624 [math.CO], 2024. See p. 18.
• Said Amrouche and Hacène Belbachir, Unimodality and linear recurrences associated with rays in the Delannoy triangle, Turkish Journal of Mathematics (2019) Vol. 44, 118-130.
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,1).

Crossrefs

Cf. A008288.

Programs

Magma

I:=[1,1,1,1,1,2]; [n le 6 select I[n] else Self(n-1)+Self(n-5)+Self(n-6): n in [1..50]]; // Vincenzo Librandi, Sep 03 2013

Mathematica

CoefficientList[Series[1 / (1 - x - x^5 - x^6), {x, 0, 50}], x] (* Vincenzo Librandi, Sep 03 2013 *)
LinearRecurrence[{1,0,0,0,1,1},{1,1,1,1,1,2},50] (* Harvey P. Dale, Mar 30 2018 *)

Formula

a(n) = a(n-1) + a(n-5) + a(n-6).

a(n) = Sum_{k=0..floor(n/5)} A008288(n-4*k, k). - Johannes W. Meijer, Jul 19 2013