A271341 Somos's sequence {a(4,n)} defined in comment in A018896.

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 10, 19, 35, 60, 156, 284, 499, 930, 1836, 7116, 21586, 52869, 115344, 356076, 972840, 3350009, 11844969, 37689894, 215136930, 785604755, 2444023816, 7985904285, 36968693334, 230985863335, 1429813280831, 6838592493455, 27144055289355, 191201731942399

Offset: 0

Author

Vladimir Shevelev and Peter J. C. Moses, Apr 04 2016

Keywords

• nonn

Comments

The sequence of the first differences begins from 9 zeros, 5 1's and 4 consecutive squares, beginning with 2^2.

A generalization see in the comment in A018896.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..318

Crossrefs

Cf. A018896, A006720, A102276, A271835, A271831, A271837, A271838, A271839.

Programs

Magma

[n le 10 select 1 else (Self(n-1)*Self(n-9) + Self(n-5)^2 )/Self(n-10): n in [1..40]]; // G. C. Greubel, Feb 21 2018

Mathematica

k = 4; Set[#, 1] & /@ Map[a[k, #] &, Range[0, 2 k + 1]]; a[k_, n_] /;
n >= 2 k + 2 := (a[k, n - 1] a[k, n - 2 k - 1] + a[k, n - k - 1]^2) / a[k, n - 2 k - 2]; Table[a[k, n], {n, 0, 42}] (* Michael De Vlieger, Apr 04 2016 *)
a[n_ /; 0 <= n <= 10] = 1; a[n_]:= a[n] = (a[n-1]*a[n-9] + a[n-5]^2)/a[n -10]; Table[a[n], {n,0,40}] (* G. C. Greubel, Feb 21 2018 *)

PARI

{a(n) = if(n< 10, 1, (a(n-1)*a(n-9) + a(n-5)^2)/a(n-10))};
for(n=0,40, print1(a(n), ", ")) \\ G. C. Greubel, Feb 21 2018

Extensions

More terms from Michael De Vlieger, Apr 04 2016