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

0,6

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

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).

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

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 *)

Prog

(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

Crossrefs

Cf. A008288.

Sequence in context: A233735 A085577 A331130 * A253241 A337972 A302979

Adjacent sequences: A121829 A121830 A121831 * A121833 A121834 A121835

Keyword

easy,nonn

Author

Jon E. Schoenfield, Aug 27 2006

Status

approved