A296359 Number of monohedral disk tilings of type C^t_{2n+1,2}.

62, 1532, 50830, 1855110, 71292624, 2833906726, 115381823442, 4782782748036, 201037496481198, 8545008347772070, 366526239773992472, 15841416797530328062, 689082764185943820494, 30139654907867753730956, 1324572400153686602854414, 58455392031254908270140098

Offset

1,1

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.

Formula

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

Mathematica

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

Prog

(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, 2*(4*n+2-i)))} \\ Andrew Howroyd, Jan 09 2018

Crossrefs

Cf. A241926, A296360, A296361, A296362.

Sequence in context: A103428 A248450 A115504 * A037962 A017778 A035726

Adjacent sequences: A296356 A296357 A296358 * A296360 A296361 A296362

Keyword

nonn

Author

N. J. A. Sloane, Dec 15 2017

Extensions

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

Status

approved