A120415 Expansion of 1/(1-x-x^3-x^6).

1, 1, 1, 2, 3, 4, 7, 11, 16, 25, 39, 59, 91, 141, 216, 332, 512, 787, 1210, 1863, 2866, 4408, 6783, 10436, 16054, 24700, 38002, 58464, 89947, 138385, 212903, 327550, 503937, 775304, 1192801, 1835123, 2823330, 4343681, 6682741, 10281375, 15817857, 24335721

Offset: 0

Author

Jon E. Schoenfield, Aug 27 2006

Keywords

• easy
• nonn

Comments

Number of compositions of n into parts 1, 3, and 6. [Joerg Arndt, Sep 03 2013]

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• K. Edwards, A Pascal-like triangle related to the tribonacci numbers, Fib. Q., 46/47 (2008/2009), 18-25.
• Index entries for linear recurrences with constant coefficients, signature (1,0,1,0,0,1).

Crossrefs

Cf. A157897.

Programs

Magma

I:=[1,1,1,2,3,4]; [n le 6 select I[n] else Self(n-1)+Self(n-3)+Self(n-6): n in [1..40]]; // Vincenzo Librandi, Sep 03 2013

Mathematica

CoefficientList[Series[1/(1-x-x^3-x^6), {x, 0, 40}], x] (* Vincenzo Librandi, Sep 03 2013 *)

SageMath

def A120415_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 1/(1-x-x^3-x^6) ).list()
A120415_list(40) # G. C. Greubel, Sep 02 2022

Formula

a(n) = a(n-1) + a(n-3) + a(n-6).

a(n) = Sum_{k=0..floor(n/2)} A157897(n-k, k). - G. C. Greubel, Sep 02 2022