A133846 a(n)*a(n-7) = a(n-1)a(n-6)+a(n-3)+a(n-4) with initial terms a(1)=...=a(7)=1.

1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 11, 19, 31, 111, 195, 283, 465, 831, 1381, 4969, 8741, 12697, 20885, 37353, 62101, 223471, 393121, 571051, 939331, 1680031, 2793151, 10051203, 17681675, 25684567, 42248981, 75564019, 125629681, 452080641, 795282225

Offset: 1

Author

Emilie Hogan, Sep 26 2007

Keywords

• easy
• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• 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 (0,0,0,0,0,46,0,0,0,0,0,-46,0,0,0,0,0,1).

Crossrefs

Cf. A072881, A092264, A133847, A133848, A133854.

Programs

Maple

a := proc(n) option remember; if n<=7 then RETURN(1); else RETURN((a(n-1)*a(n-6)+a(n-3)+a(n-4))/a(n-7)); fi; end;

Mathematica

nxt[{a_,b_,c_,d_,e_,f_,g_}]:={b,c,d,e,f,g,(g*b+e+d)/a}; Transpose[ NestList[ nxt,{1,1,1,1,1,1,1},40]][[1]] (* or *) LinearRecurrence[ {0,0,0,0,0,46,0,0,0,0,0,-46,0,0,0,0,0,1},{1,1,1,1,1,1,1,3,5,7,11,19,31,111,195,283,465,831},40] (* Harvey P. Dale, Aug 21 2014 *)

PARI

a(k=7, 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 -45*x^6 -43*x^7 -41*x^8 -39*x^9 -35*x^10 -27*x^11 +31*x^12 +19*x^13 +11*x^14 +7*x^15 +5*x^16 +3*x^17) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 -45*x^6 +x^12)) + O(x^50)) \\ Colin Barker, Jul 18 2016

Formula

G.f.: x*(1 +x +x^2 +x^3 +x^4 +x^5 -45*x^6 -43*x^7 -41*x^8 -39*x^9 -35*x^10 -27*x^11 +31*x^12 +19*x^13 +11*x^14 +7*x^15 +5*x^16 +3*x^17) / ((1 -x)*(1 +x)*(1 -x +x^2)*(1 +x +x^2)*(1 -45*x^6 +x^12)). - Colin Barker, Jul 18 2016