A133848 a(n)*a(n-11) = a(n-1)*a(n-10)+a(n-5)+a(n-6) with initial terms a(1)=...=a(11)=1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 9, 11, 15, 23, 35, 51, 71, 239, 411, 587, 767, 951, 1325, 2075, 3201, 4703, 6581, 22185, 38165, 54521, 71253, 88361, 123141, 192889, 297605, 437289, 611941, 2062927, 3548881, 5069803, 6625693, 8216551, 11450719

Offset: 1

Author

Emilie Hogan, Sep 26 2007

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..5091
• 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 (0,0,0,0,0,0,0,0,0,94,0,0,0,0,0,0,0,0,0,-94,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A072881, A092264, A133846, A133847, A133854.

Programs

Maple

a := proc(n) option remember; if n<=11 then RETURN(1); else RETURN((a(n-1)*a(n-10)+a(n-5)+a(n-6))/a(n-11)); fi; end;

Mathematica

Rest@ CoefficientList[Series[x (1 + x + x^2 + x^3 + x^4 + x^5 + x^6 + x^7 + x^8 + x^9 - 93 x^10 - 91 x^11 - 89 x^12 - 87 x^13 - 85 x^14 - 83 x^15 - 79 x^16 - 71 x^17 - 59 x^18 - 43 x^19 + 71 x^20 + 51 x^21 + 35 x^22 + 23 x^23 + 15 x^24 + 11 x^25 + 9 x^26 + 7 x^27 + 5 x^28 + 3 x^29)/((1 - x) (1 + x) (1 - x + x^2 - x^3 + x^4) (1 + x + x^2 + x^3 + x^4) (1 - 93 x^10 + x^20)), {x, 0, 47}], x] (* Michael De Vlieger, Jul 18 2016 *)

PARI

a(k=11, 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 -93*x^10 -91*x^11 -89*x^12 -87*x^13 -85*x^14 -83*x^15 -79*x^16 -71*x^17 -59*x^18 -43*x^19 +71*x^20 +51*x^21 +35*x^22 +23*x^23 +15*x^24 +11*x^25 +9*x^26 +7*x^27 +5*x^28 +3*x^29) / ((1 -x)*(1 +x)*(1 -x +x^2 -x^3 +x^4)*(1 +x +x^2 +x^3 +x^4)*(1 -93*x^10 +x^20)) + O(x^60)) \\ Colin Barker, Jul 18 2016

Formula

Sequence also generated by the linear recurrence 94*(u(n-10)-u(n-20))+u(n-30) with the initial 30 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 -93*x^10 -91*x^11 -89*x^12 -87*x^13 -85*x^14 -83*x^15 -79*x^16 -71*x^17 -59*x^18 -43*x^19 +71*x^20 +51*x^21 +35*x^22 +23*x^23 +15*x^24 +11*x^25 +9*x^26 +7*x^27 +5*x^28 +3*x^29) / ((1 -x)*(1 +x)*(1 -x +x^2 -x^3 +x^4)*(1 +x +x^2 +x^3 +x^4)*(1 -93*x^10 +x^20)). - Colin Barker, Jul 18 2016