login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,8

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

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).

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

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 *)

PROG

(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

CROSSREFS

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

Sequence in context: A327461 A126116 A161423 * A056208 A323065 A225421

Adjacent sequences:  A133843 A133844 A133845 * A133847 A133848 A133849

KEYWORD

easy,nonn

AUTHOR

Emilie Hogan, Sep 26 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 18 04:44 EST 2019. Contains 329248 sequences. (Running on oeis4.)