A133854 a(n)*a(n-13) = a(n-1)*a(n-12)+a(n-6)+a(n-7) with initial terms a(1)=...=a(13)=1.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 9, 11, 13, 17, 25, 37, 53, 73, 97, 321, 549, 781, 1017, 1257, 1501, 1995, 2985, 4471, 6453, 8931, 11905, 39433, 67457, 95977, 124993, 154505, 184513, 245273, 367041, 549817, 793601, 1098393, 1464193, 4849891
Offset: 1
Links
- Seiichi Manyama, Table of n, a(n) for n = 1..5754
- 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 (0,0,0,0,0,0,0,0,0,0,0,124,0,0,0,0,0,0,0,0,0,0,0,-124,0,0,0,0,0,0,0,0,0,0,0,1).
Programs
-
Maple
a := proc(n) option remember; if n<=13 then RETURN(1); else RETURN((a(n-1)*a(n-12)+a(n-6)+a(n-7))/a(n-13)); fi; end;
-
Mathematica
RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]== a[8]== a[9]== a[10]== a[11]== a[12]==a[13]==1,a[n]==(a[n-1]a[n-12]+a[n-6]+ a[n-7])/ a[n-13]},a,{n,50}] (* Harvey P. Dale, Nov 24 2015 *) -
PARI
a(k=13, 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 +x^8 +x^9 +x^10 +x^11 -123*x^12 -121*x^13 -119*x^14 -117*x^15 -115*x^16 -113*x^17 -111*x^18 -107*x^19 -99*x^20 -87*x^21 -71*x^22 -51*x^23 +97*x^24 +73*x^25 +53*x^26 +37*x^27 +25*x^28 +17*x^29 +13*x^30 +11*x^31 +9*x^32 +7*x^33 +5*x^34 +3*x^35) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x^2)*(1 +x +x^2)*(1 -x^2 +x^4)*(1 +11*x^6 -x^12)*(1 -11*x^6 -x^12)) + O(x^60)) \\ Colin Barker, Jul 18 2016
Formula
Sequence also generated by the linear recurrence 124*(u(n-12)-u(n-24))+u(n-36) with the initial 36 terms given by the quadratic recurrence.
G.f.: x*(1 +x +x^2 +x^3 +x^4 +x^5 +x^6 +x^7 +x^8 +x^9 +x^10 +x^11 -123*x^12 -121*x^13 -119*x^14 -117*x^15 -115*x^16 -113*x^17 -111*x^18 -107*x^19 -99*x^20 -87*x^21 -71*x^22 -51*x^23 +97*x^24 +73*x^25 +53*x^26 +37*x^27 +25*x^28 +17*x^29 +13*x^30 +11*x^31 +9*x^32 +7*x^33 +5*x^34 +3*x^35) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x^2)*(1 +x +x^2)*(1 -x^2 +x^4)*(1 +11*x^6 -x^12)*(1 -11*x^6 -x^12)). - Colin Barker, Jul 18 2016