A017838 Expansion of 1/(1-x^5-x^6-x^7).

1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 1, 2, 3, 2, 1, 1, 3, 6, 7, 6, 4, 5, 10, 16, 19, 17, 15, 19, 31, 45, 52, 51, 51, 65, 95, 128, 148, 154, 167, 211, 288, 371, 430, 469, 532, 666, 870, 1089, 1270, 1431, 1667, 2068, 2625, 3229

Offset

0,12

Comments

Number of compositions (ordered partitions) of n into parts 5, 6 and 7. - Ilya Gutkovskiy, May 25 2017

Links

Muniru A Asiru, Table of n, a(n) for n = 0..700

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

Formula

a(n) = a(n-5) + a(n-6) + a(n-7). - Vincenzo Librandi, Mar 23 2011

a(n) = Sum_{k=0..floor(n/4)} Sum_{j=0..k} binomial(j,n-5*k-j)*binomial(k,j). - Vladimir Kruchinin, Nov 16 2011

Maple

seq(coeff(series(1/(1-x^5-x^6-x^7), x, n+1), x, n), n=0..60); # Muniru A Asiru, Jul 04 2018

Mathematica

CoefficientList[Series[1/(1 - x^5 - x^6 - x^7), {x, 0, 60}], x] (* or *) LinearRecurrence[{0, 0, 0, 0, 1, 1, 1}, {1, 0, 0, 0, 0, 1, 1}, 60] (* Harvey P. Dale, Jun 28 2011 *)

Prog

(Maxima) a(n):=sum(sum(binomial(j, n-5*k-j)*binomial(k, j), j, 0, k), k, 0, n/4); /* Vladimir Kruchinin, Nov 16 2011 */

Crossrefs

Sequence in context: A086437 A027907 A026323 * A181567 A058294 A323834

Adjacent sequences: A017835 A017836 A017837 * A017839 A017840 A017841

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved