A296362 - OEIS

%I #20 Jun 14 2018 16:18:51

%S 2,1532,6402,19884,51128,115188,235180,445096,792822,1343814,2185396,

%T 3431466,5227806,7758398,11251894,15989150,22311572,30630012,41434474,

%U 55305224,72924016,95086728,122717140,156881256,198802766,249880274,311704608,386077910

%N Number of monohedral disk tilings of type C^t_{5,n}.

%H Lars Blomberg, <a href="/A296362/b296362.txt">Table of n, a(n) for n = 1..1000</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..10} A241926(i, n*(10-i)) for n > 1. - _Andrew Howroyd_, Jan 09 2018

%F G.f.: 2*x*(1 + 763*x + 905*x^2 + 1871*x^3 + 2142*x^4 + 2318*x^5 + 2333*x^6 + 1022*x^7 + 602*x^8 - 348*x^9 - 1422*x^10 - 1599*x^11 - 2949*x^12 - 3041*x^13 - 2413*x^14 - 2329*x^15 - 316*x^16 - 538*x^17 + 175*x^18 + 703*x^19 + 562*x^20 + 1446*x^21 + 852*x^22 + 147*x^23 + 48*x^24 - 646*x^25 - 6*x^26 + 224*x^27 + 16*x^28 + 184*x^29 - 310*x^30 + 107*x^31) / ((1 - x)^9*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^3*(1 + x^3 + x^6)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)) (conjectured). - _Colin Barker_, Jan 09 2018

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

%t a[1] = 2; a[n_] := 2*Sum[ U[i, n*(10 - i)], {i, 0, 10}];

%t Array[a, 30] (* _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*if(n<2, n==1, sum(i=0, 10, U(i,n*(10-i))))} \\ _Andrew Howroyd_, Jan 09 2018

%Y Cf. A241926, A296359, A296360, A296361.

%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