A350513 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

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