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%I #32 Jul 05 2018 02:43:54
%S 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,
%T 52,51,51,65,95,128,148,154,167,211,288,371,430,469,532,666,870,1089,
%U 1270,1431,1667,2068,2625,3229
%N Expansion of 1/(1-x^5-x^6-x^7).
%C Number of compositions (ordered partitions) of n into parts 5, 6 and 7. - _Ilya Gutkovskiy_, May 25 2017
%H Muniru A Asiru, <a href="/A017838/b017838.txt">Table of n, a(n) for n = 0..700</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,1,1,1).
%F a(n) = a(n-5) + a(n-6) + a(n-7). - _Vincenzo Librandi_, Mar 23 2011
%F 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
%p 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
%t 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 *)
%o (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 */
%K nonn,easy
%O 0,12
%A _N. J. A. Sloane_
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