A025258 a(n) = a(1)*a(n-1) + a(2)*a(n-2) + ... + a(n-3)*a(3) for n >= 4, with initial terms 1, -1, 1, 1.

1, -1, 1, 1, 0, 0, 2, 3, 1, 2, 11, 17, 12, 25, 81, 127, 134, 276, 696, 1118, 1492, 3005, 6607, 10935, 16766, 33047, 67249, 114611, 190706, 369424, 719956, 1258251, 2196855, 4201958, 8000409, 14263679, 25620508, 48585009, 91421253, 165467590

Offset

1,7

Links

Michael De Vlieger, Table of n, a(n) for n = 1..3544

Paul Barry, Riordan Pseudo-Involutions, Continued Fractions and Somos 4 Sequences, arXiv:1807.05794 [math.CO], 2018.

Formula

Conjecture: -n*a(n) +(2*n-3)*a(n-1) +3*(-n+3)*a(n-2) +3*(2*n-9)*a(n-3) +(-n+6)*a(n-4)=0. - R. J. Mathar, Feb 25 2015

From Seiichi Manyama, Dec 16 2025: (Start)

G.f. A(x) satisfies A(x) = x * (1-x + x^2/(1-A(x))).

G.f.: 2*x*(1-x+x^2)/(1+x-x^2 + sqrt(1-2*x+3*x^2-6*x^3+x^4)). (End)

Mathematica

Nest[Function[a, Append[a, Inner[Times, #1, #2, Plus] & @@ Transpose @@ {Array[{a[[#]], a[[-#]]} &, Length[a] - 2 ]}] ], {1, -1, 1, 1}, 36] (* Michael De Vlieger, Oct 17 2018 *)

Crossrefs

Sequence in context: A059379 A065487 A341287 * A118846 A361157 A082503

Adjacent sequences: A025255 A025256 A025257 * A025259 A025260 A025261

Keyword

sign

Author

Clark Kimberling

Status

approved