A064268 a(n) = (a(n-1) * a(n-6) + 2 * a(n-3) * a(n-4)) / a(n-7). a(1) = ... = a(7) = 1. Somos-7 variation.

1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 13, 43, 113, 521, 1241, 3681, 23657, 177721, 679505, 4674203, 27273277, 275517767, 3496390229, 37043734803, 226196947873, 4391322667601, 81041508965617, 1433151398896001, 25397505914206225, 472652420405241521, 9156799134584424289, 499597377081528480243

Offset

1,8

Comments

In general, suppose a(n)*a(n-7) = c1*a(n-1)*a(n-6) + c2*a(n-3)*a(n-4) for all n and constants c1,c2. Define u(n) = a(n)*a(n+5)/(a(n+2)*a(n+3)) which satisfies the generalized Lyness recursion u(n) = (c1*u(n-1) + c2)/u(n-2) for all n. For this sequence c1=1, c2=2, u(n) is (1, 1, 3, 5, 7/3, 13/15, 43/35, ...) and satisfies u(n) = (u(n-1) + 2)/u(n-2). See A076839 for Lyness references. - Michael Somos, Sep 26 2022

Links

Harry J. Smith, Table of n, a(n) for n = 1..100

Index entries for two-way infinite sequences

Formula

a(8-n) = a(n).

Mathematica

RecurrenceTable[{a[1]==a[2]==a[3]==a[4]==a[5]==a[6]==a[7]==1, a[n] == (a[n-1]a[n-6]+2a[n-3]a[n-4])/a[n-7]}, a, {n, 30}] (* Harvey P. Dale, Nov 26 2015 *)

Prog

(PARI) {a(n) = if( n<1, a(8-n), if( n<8, 1, (a(n-1) * a(n-6) + 2 * a(n-3) * a(n-4)) / a(n-7)))};
(PARI) { a7=a6=a5=a4=a3=a2=a1=a=1; for (n=1, 100, if (n>7, a=(a1*a6 + 2*a3*a4)/a7; a7=a6; a6=a5; a5=a4; a4=a3; a3=a2; a2=a1; a1=a); write("b064268.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 10 2009
(Magma) I:=[1, 1, 1, 1, 1, 1, 1]; [n le 7 select I[n] else (Self(n-1)*Self(n-6) + 2*Self(n-3)*Self(n-4))/Self(n-7): n in [1..30]]; // G. C. Greubel, Feb 21 2018

Crossrefs

Cf. A006723, A076839.

Sequence in context: A163080 A141414 A236464 * A235873 A118743 A225226

Adjacent sequences: A064265 A064266 A064267 * A064269 A064270 A064271

Keyword

nonn,easy

Author

Michael Somos, Sep 24 2001

Status

approved