A375922 a(n) = (a(n-3)*a(n-9) + a(n-1)*a(n-11))/a(n-12) with a(0) = ... = a(11) = 1.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 79, 163, 490, 972, 1785, 4270, 9483, 19251, 41603, 100739, 259579, 997371, 3297339, 12754875, 33992883, 94594611, 363844867, 1139238123, 3317604094, 12075672425, 56552033036, 254310500890

Offset

0,13

Comments

Sequence defined by recursion derived from Sato discrete tau function.

When extended to n<0 by a(n) = a(13-n) for all n in Z, then also a(n+6)*a(n-6) = a(n+5)*a(n-5) + a(n+3)*a(n-3) for all n in Z. It is a Gale-Robinson sequence. - Michael Somos, Nov 28 2024

Links

Alois P. Heinz, Table of n, a(n) for n = 0..345

Mohamed Bensaid, Sato tau functions and construction of Somos sequence, arXiv:2409.05911 [math.NT], 2024.

Eric Weisstein's World of Mathematics, Somos Sequence.

Maple

a:= proc(n) option remember; `if`(n<12, 1,
     (a(n-3)*a(n-9)+a(n-1)*a(n-11))/a(n-12))
    end:
seq(a(n), n=0..42);  # Alois P. Heinz, Sep 02 2024

Mathematica

a[n_] := a[n] = If[n < 12, 1, (a[n-3]*a[n-9] + a[n-1]*a[n-11]) / a[n-12]]; Array[a, 40, 0] (* Amiram Eldar, Sep 02 2024 *)

Prog

(PARI) seq(n)={my(a=vector(n+1, i, 1)); for(n=13, #a, a[n] =(a[n-3]*a[n-9]+a[n-1]*a[n-11])/a[n-12]); a} \\ Andrew Howroyd, Sep 03 2024

Crossrefs

Cf. A375621.

Sequence in context: A101913 A352042 A121653 * A238434 A061418 A355909

Adjacent sequences: A375919 A375920 A375921 * A375923 A375924 A375925

Keyword

nonn

Author

Mohamed Bensaid, Sep 02 2024

Status

approved