A385977 Length of the long leg of the triangles defined in A377725.

4, 112, 3444, 114720, 3883684, 131852560, 4478648724, 152139554112, 5168250745924, 175568295786160, 5964153281301684, 202605640210401120, 6882627596048598244, 233806732521557580112, 7942546277531426709204, 269812766700017940393600, 9165691521502509968254084

Offset

0,1

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (41,-246,246,-41,1).

Formula

a(n) = 2 * A002315(n) * (A002315(n) + 1).

From Andrew Howroyd, Nov 16 2025: (Start)

a(n) = 4*A377016(n).

G.f.: 4*(1 + 3*x)*(1 - 16*x + 7*x^2)/((1 - x)*(1 - 34*x + x^2)*(1 - 6*x + x^2)). (End)

Mathematica

LinearRecurrence[{41, -246, 246, -41, 1}, {4, 112, 3444, 114720, 3883684}, 20] (* Paolo Xausa, Jan 15 2026 *)

Prog

(PARI) a(n)=my(t=polcoef((1 + x)/(1 - 6*x + x^2) + O(x*x^n), n)); 2*t*(t + 1); \\ Andrew Howroyd, Nov 16 2025

Crossrefs

Cf. A002315, A377725 (short leg), A378380, A378386, A379509.

Sequence in context: A378803 A158450 A063406 * A361543 A221625 A013151

Adjacent sequences: A385974 A385975 A385976 * A385978 A385979 A385980

Keyword

nonn,easy

Author

Sean A. Irvine, Jul 13 2025

Extensions

Offset corrected by Andrew Howroyd, Nov 16 2025

Status

approved