A296360 Number of monohedral disk tilings of type C^t_{2n+1,3}.

116, 6402, 446930, 34121322, 2741227176, 227759341712, 19382568941318, 1679333068357460, 147541888215426742, 13107891004266127974, 1175188298096727647322, 106164291028322202227232, 9652457243380891557169712, 882443342536355491502025678

Offset: 1

Author

N. J. A. Sloane, Dec 15 2017

Keywords

• nonn

Links

• Lars Blomberg, Table of n, a(n) for n = 1..100
• Joel Anthony Haddley, Stephen Worsley, Infinite families of monohedral disk tilings, arXiv:1512.03794v2 [math.MG], 2015-2016.

Crossrefs

Cf. A241926, A296359, A296361, A296362.

Programs

Mathematica

U[n_, k_] := DivisorSum[GCD[n, k], EulerPhi[#]*Binomial[(n + k)/#, n/#]/(n + k) &];
a[n_] := 2*Sum[U[i, 3*(4*n + 2 - i)], {i, 0, 4*n + 2}];
Array[a, 16] (* Jean-François Alcover, Jun 14 2018, after Andrew Howroyd *)

PARI

\\ here U is A241926
U(n,k)={sumdiv(gcd(n,k), d, eulerphi(d)*binomial((n+k)/d, n/d)/(n+k))}
a(n)={2*sum(i=0, 4*n+2, U(i,3*(4*n+2-i)))} \\ Andrew Howroyd, Jan 09 2018

Formula

a(n) = 2*Sum_{i=0..4*n+2} A241926(i, 3*(4*n+2-i)). - Andrew Howroyd, Jan 09 2018

Extensions

Terms a(6) and beyond from Lars Blomberg, Jan 09 2018