|
%I #21 Jul 18 2016 05:53:17
%S 1,1,1,1,1,3,5,9,17,65,117,227,449,1737,3137,6105,12097,46819,84565,
%T 164593,326161,1262361,2280101,4437891,8794241,34036913,61478145,
%U 119658449,237118337,917734275,1657629797,3226340217,6393400849
%N a(n)*a(n-5) = a(n-1)*a(n-4)+a(n-2)+a(n-3), with initial terms a(1) = ... = a(5) = 1.
%H Seiichi Manyama, <a href="/A092264/b092264.txt">Table of n, a(n) for n = 1..2801</a>
%H P. Heideman and E. Hogan, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v15i1r54">A new family of Somos-like recurrences</a>, The Electronic Journal of Combinatorics, Volume 15 (2008), #R54.
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 28, 0, 0, 0, -28, 0, 0, 0, 1).
%F a(1)=1, a(2)=1, a(3)=1, a(4)=1, a(5)=1, a(6)=3, a(7)=5, a(8)=9, a(9)=17, a(10)=65, a(11)=117, a(12)=227, a(n)=28*a(n-4)-28*a(n-8)+a(n-12). - _Harvey P. Dale_, Aug 08 2013
%F G.f.: x*(1 +x +x^2 +x^3 -27*x^4 -25*x^5 -23*x^6 -19*x^7 +17*x^8 +9*x^9 +5*x^10 +3*x^11) / ((1 -x)*(1 +x)*(1 +x^2)*(1 +5*x^2 -x^4)*(1 -5*x^2 -x^4)). - _Colin Barker_, Jul 18 2016
%p R := proc(n) option remember; if n<5 then 1 else RETURN((R(n-1)*R(n-4)+R(n-2)+R(n-3))/R(n-5)); fi; end;
%t RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==a[5]==1,a[n]==(a[n-1]a[n-4]+a[n-2]+a[n-3])/a[n-5]},a,{n,40}] (* or *) LinearRecurrence[ {0,0,0,28,0,0,0,-28,0,0,0,1},{1,1,1,1,1,3,5,9,17,65,117,227},40] (* _Harvey P. Dale_, Aug 08 2013 *)
%o (PARI) a(k=5, n) = {K = (k-1)/2; vds = vector(n); for (i=1, 2*K+1, vds[i] = 1;); for (i=2*K+2, n, vds[i] = (vds[i-1]*vds[i-2*K]+vds[i-K]+vds[i-K-1])/vds[i-2*K-1];); for (i=1, n, print1(vds[i], ","););} \\ _Michel Marcus_, Nov 01 2012
%o (PARI) Vec(x*(1 +x +x^2 +x^3 -27*x^4 -25*x^5 -23*x^6 -19*x^7 +17*x^8 +9*x^9 +5*x^10 +3*x^11) / ((1 -x)*(1 +x)*(1 +x^2)*(1 +5*x^2 -x^4)*(1 -5*x^2 -x^4)) + O(x^50)) \\ _Colin Barker_, Jul 18 2016
%Y Cf. A072881, A133846, A133847, A133848, A133854.
%K nonn,easy
%O 1,6
%A Paul Heideman (ppheideman(AT)wisc.edu), Feb 19 2004
|
