A350513 Number of 2 X n rectangular Celtic knots (up to rotations and symmetries).

3, 21, 648, 15552, 404595, 10812528, 290993472, 7849029276, 211855234563, 5719493462076, 154420985682648, 4169319089851512, 112571188876032435, 3039418274650387848, 82064259021919140432, 2215734684425617523796, 59824833697843168341123, 1615270484817096465311316

Offset

1,1

Links

Table of n, a(n) for n=1..18.

Jessica Connor and Nick Ward, Celtic Knot Theory

Formula

a(n) = (3^(3*n-2) + 3^((3*n-2)/2) + 3^(2*n-1) + 3^(3*n/2))/4 for even n > 2;

a(n) = (3^(3*n-2) + 3^((3*n-1)/2) + 3^(2*n-1) + 3^((3*n-1)/2))/4 for odd n.

a(n) = (3^(3*n-2) + 3^floor((3*n-1)/2) + 3^(2*n-1) + 3^floor(3*n/2))/4 for n <> 2.

Prog

(PARI) a(n) = if(n==2, 21, (3^(3*n-2) + 3^((3*n-1)\2) + 3^(2*n-1) + 3^(3*n\2))/4) \\ Andrew Howroyd, Jan 03 2022

Crossrefs

Cf. A032120 (1 X n Celtic knots).

Sequence in context: A181003 A093549 A012044 * A098918 A001699 A291967

Adjacent sequences: A350510 A350511 A350512 * A350514 A350515 A350516

Keyword

nonn

Author

Philippe Gibone, Jan 02 2022

Status

approved