A133847 a(n)*a(n-9) = a(n-1)*a(n-8)+a(n-4)+a(n-5) with initial terms a(1)=...=a(9)=1.
1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 9, 13, 21, 33, 49, 169, 293, 421, 553, 823, 1365, 2179, 3265, 11289, 19585, 28153, 36993, 55081, 91393, 145929, 218689, 756163, 1311861, 1885783, 2477929, 3689557, 6121925, 9775033, 14648881, 50651601, 87875061
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..4390
- P. Heideman and E. Hogan, A New Family of Somos-Like Recurrences, arXiv:0709.2529 [math.CO], 2007-2009.
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,68,0,0,0,0,0,0,0,-68,0,0,0,0,0,0,0,1).
Programs
-
Maple
a := proc(n) option remember; if n<=9 then RETURN(1); else RETURN((a(n-1)*a(n-8)+a(n-4)+a(n-5))/a(n-9)); fi; end;
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Mathematica
RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]==a[8]==a[9]==1,a[n]==(a[n-1]a[n-8]+a[n-4]+a[n-5])/a[n-9]},a,{n,50}] (* or *) LinearRecurrence[{0,0,0,0,0,0,0,68,0,0,0,0,0,0,0,-68,0,0,0,0,0,0,0,1},{1,1,1,1,1,1,1,1,1,3,5,7,9,13,21,33,49,169,293,421,553,823,1365,2179},50] (* Harvey P. Dale, Jan 14 2016 *) -
PARI
a(k=9, 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 +x^4 +x^5 +x^6 +x^7 -67*x^8 -65*x^9 -63*x^10 -61*x^11 -59*x^12 -55*x^13 -47*x^14 -35*x^15 +49*x^16 +33*x^17 +21*x^18 +13*x^19 +9*x^20 +7*x^21 +5*x^22 +3*x^23) / ((1 -x)*(1 +x)*(1 +x^2)*(1 +x^4)*(1 -67*x^8 +x^16)) + O(x^50)) \\ Colin Barker, Jul 18 2016
Formula
Sequence also generated by the linear recurrence 68*(u(n-8)-u(n-16))+u(n-24) with the initial 24 terms given by the quadratic recurrence.
G.f.: x*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 -67*x^8 -65*x^9 -63*x^10 -61*x^11 -59*x^12 -55*x^13 -47*x^14 -35*x^15 +49*x^16 +33*x^17 +21*x^18 +13*x^19 +9*x^20 +7*x^21 +5*x^22 +3*x^23) / ((1 -x)*(1 +x)*(1 +x^2)*(1 +x^4)*(1 -67*x^8 +x^16)). - Colin Barker, Jul 18 2016