A017828 - OEIS

A017828

Expansion of 1/(1-x^4-x^5-x^6).

1, 0, 0, 0, 1, 1, 1, 0, 1, 2, 3, 2, 2, 3, 6, 7, 7, 7, 11, 16, 20, 21, 25, 34, 47, 57, 66, 80, 106, 138, 170, 203, 252, 324, 414, 511, 625, 779, 990, 1249, 1550, 1915, 2394, 3018, 3789, 4714, 5859, 7327, 9201, 11521

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OFFSET

0,10

COMMENTS

Number of compositions (ordered partitions) of n into parts 4, 5 and 6. - Ilya Gutkovskiy, May 25 2017

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 1, 1, 1).

FORMULA

a(n) = a(n-6) + a(n-5) + a(n-4). - Jon E. Schoenfield, Aug 07 2006

a(n) = Sum_{k=0..floor(n/3)}, Sum_{j=0..k} binomial(j, n-4*k-j)*binomial(k,j). - Vladimir Kruchinin, Nov 16 2011

MATHEMATICA

LinearRecurrence[{0, 0, 0, 1, 1, 1}, {1, 0, 0, 0, 1, 1}, 60] (* Vincenzo Librandi, Nov 18 2011 *)

CoefficientList[Series[1/(1-x^4-x^5-x^6), {x, 0, 50}], x] (* Harvey P. Dale, Feb 28 2024 *)

PROG

(Maxima) a(n):=sum(sum(binomial(j, n-4*k-j)*binomial(k, j), j, 0, k), k, 0, n/3); /* Vladimir Kruchinin, Nov 16 2011 */

(Magma) I:=[1, 0, 0, 0, 1, 1]; [n le 6 select I[n] else Self(n-6)+Self(n-5)+Self(n-4): n in [1..60]]; // Vincenzo Librandi, Nov 18 2011

(PARI) Vec(1/(1-x^4-x^5-x^6)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

CROSSREFS

Sequence in context: A177865 A307835 A341651 * A140087 A174329 A295312

Adjacent sequences: A017825 A017826 A017827 * A017829 A017830 A017831

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved