A092264 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.
1, 1, 1, 1, 1, 3, 5, 9, 17, 65, 117, 227, 449, 1737, 3137, 6105, 12097, 46819, 84565, 164593, 326161, 1262361, 2280101, 4437891, 8794241, 34036913, 61478145, 119658449, 237118337, 917734275, 1657629797, 3226340217, 6393400849
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..2801
- P. Heideman and E. Hogan, A new family of Somos-like recurrences, The Electronic Journal of Combinatorics, Volume 15 (2008), #R54.
- Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 28, 0, 0, 0, -28, 0, 0, 0, 1).
Programs
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Maple
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;
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Mathematica
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 *) -
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 -
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
Formula
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
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