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Number of monohedral disk tilings of type C^t_{2n+1,3}.
4

%I #20 Jun 14 2018 05:14:00

%S 116,6402,446930,34121322,2741227176,227759341712,19382568941318,

%T 1679333068357460,147541888215426742,13107891004266127974,

%U 1175188298096727647322,106164291028322202227232,9652457243380891557169712,882443342536355491502025678

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

%H Lars Blomberg, <a href="/A296360/b296360.txt">Table of n, a(n) for n = 1..100</a>

%H Joel Anthony Haddley, Stephen Worsley, <a href="https://arxiv.org/abs/1512.03794">Infinite families of monohedral disk tilings</a>, arXiv:1512.03794v2 [math.MG], 2015-2016.

%F a(n) = 2*Sum_{i=0..4*n+2} A241926(i, 3*(4*n+2-i)). - _Andrew Howroyd_, Jan 09 2018

%t U[n_, k_] := DivisorSum[GCD[n, k], EulerPhi[#]*Binomial[(n + k)/#, n/#]/(n + k) &];

%t a[n_] := 2*Sum[U[i, 3*(4*n + 2 - i)], {i, 0, 4*n + 2}];

%t Array[a, 16] (* _Jean-François Alcover_, Jun 14 2018, after _Andrew Howroyd_ *)

%o (PARI) \\ here U is A241926

%o U(n,k)={sumdiv(gcd(n,k), d, eulerphi(d)*binomial((n+k)/d, n/d)/(n+k))}

%o a(n)={2*sum(i=0, 4*n+2, U(i,3*(4*n+2-i)))} \\ _Andrew Howroyd_, Jan 09 2018

%Y Cf. A241926, A296359, A296361, A296362.

%K nonn

%O 1,1

%A _N. J. A. Sloane_, Dec 15 2017

%E Terms a(6) and beyond from _Lars Blomberg_, Jan 09 2018