A352625 A (25,-29) Somos-4 sequence.

1, 2, 7, 59, 1529, 83313, 7869898, 1687054711, 1123424582771, 1662315215971057, 4257998884448335457, 23385756731869683322514, 397068399296019032727466599, 15886280085653574502219650145963, 1107464108502549897934954766675333353, 157131202095317153373302215985417166354641

Offset: 0

Author

Michael Somos, Mar 24 2022

Keywords

• nonn

Comments

Hankel transform of A188314 with first term omitted.

Examples

			G.f.: 1 + 2*x + 7*x^2 + 59*x^3 + 1529*x^4 + 83313*x^5 + ...
a(2) = 7 = 2*16 - 5*5 = det([2, 5; 5, 16]).
		

Crossrefs

Cf. A006720, A188313, A188314.

Programs

Mathematica

b[ n_] := If[OddQ[n], a[-(n-1)/2], a[n/2-1]]; a[ n_] := If[-3<=n<=1, {23, 3, 1, 1, 2}[[n+4]], 2*b[1-n]^3*b[2-n] + b[-n]^2*(b[2-n]*b[3-n] - b[1-n]*b[4-n])];

Formula

a(n) = (25*a(n-1)*a(n-3) - 29*a(n-2)^2)/a(n-4) for all n in Z.

a(n) = (29*a(n-1)*a(n-4) - 13*a(n-2)*a(n-3))/a(n-5) for all n in Z.

a(n) = b(1-2*n) = b(2*n+2) = A188313(-1-n) for all n in Z where b(n) = A006720(n).