A378817 Hankel sequence transform of A378816.

-1, -5, 6, -10, 11, -1, 1, 17, -18, 22, -23, 1, -1, -29, 30, -34, 35, -1, 1, 41, -42, 46, -47, 1, -1, -53, 54, -58, 59, -1, 1, 65, -66, 70, -71, 1, -1, -77, 78, -82, 83, -1, 1, 89, -90, 94, -95, 1, -1, -101, 102, -106, 107, -1, 1, 113, -114, 118, -119

Offset

0,2

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-3,0,2,0,-1).

Formula

G.f.: (-1 - 5*x + 8*x^2 - 4*x^4 + 4*x^5 - x^6 - x^7)/(1 - x^2 + x^4)^2.

a(n) = 2*a(n-2) - 3*a(n-4) + 2*a(n-6) - a(n-8).

a(12*n) = -1.

a(5+12*n) = -1.

a(6+12*n) = 1.

a(11+12*n) = 1.

a(1+12*n) = -5-24*n.

a(2+12*n) = 6+24*n.

a(3+12*n) = -10-24*n.

a(4+12*n) = 11+24*n.

a(7+12*n) = 17+24*n.

a(8+12*n) = -18-24*n.

a(9+12*n) = 22+24*n.

a(10+12*n) = -23-24*n.

Mathematica

LinearRecurrence[{0, 2, 0, -3, 0, 2, 0, -1}, {-1, -5, 6, -10, 11, -1, 1, 17}, 100] (* Paolo Xausa, Jan 28 2025 *)

Prog

(PARI) a(n) =  (1+(2*n+3-n%3)*((n%6)*((n+1)%6)>0))*(-1)^(n+1+ceil(n/6))

Crossrefs

Cf. A378783, A378816.

Sequence in context: A019205 A379207 A191472 * A189056 A340325 A247561

Adjacent sequences: A378814 A378815 A378816 * A378818 A378819 A378820

Keyword

sign,easy

Author

Thomas Scheuerle, Dec 08 2024

Status

approved