The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A273090 Rectangular array A read by upward antidiagonals in which the entry A(n,k) in row k and column n gives the number of families of symmetric radially generated monohedral tilings of the disk (each tiling contains 2*(2*n+1)*k congruent tiles), k >= 1, n >= 1. 0
 2, 62, 2, 116, 1532, 2, 200, 6402, 50830, 2, 318, 19884, 446930, 1855110, 2, 476, 51128, 2460462, 34121322, 71292624, 2, 682, 115188, 10106370, 332112068, 2741227176, 2833906726, 2, 946, 235180, 33905948, 2177193500, 47162138964 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Enumeration is equivalent to counting beaded necklaces of a certain class (see A047996). For details and definitions, see the arXiv preprint by Haddley and Worsley. LINKS Joel Haddley, Stephen Worsley, Infinite families of monohedral disk tilings, arXiv preprint arXiv:1512.03794v2 [math.MG], 2016. FORMULA A(1,n) = 2, A(k,n) = 2*Sum_{i=0..2*(2*n+1)}Sum_{d | i, d | (2*(2*n+1)-i)*k} (phi(d)/i)*binomial((2*(2*n+1)-i)*k/d+i/d-1, i/d-1), k >= 2, n >= 1 [Haddley, Worsley, Proposition 5.1]. EXAMPLE Array begins: .    2       2         2            2              2                 2 .   62    1532     50830      1855110       71292624        2833906726 .  116    6402    446930     34121322     2741227176      227759341712 .  200   19884   2460462    332112068    47162138964     6926365932512 .  318   51128  10106370   2177193500   493416845604   115646287581042 .  476  115188  33905948  10874491594  3668999040616  1280224897307324 MATHEMATICA a[1, n_] := 2; a[k_, n_] := 2*(1 + Sum[(1/i)*Sum[EulerPhi[d]*Binomial[(2*(2*n + 1) - i)*k/d + i/d - 1, i/d - 1], {d, Divisors[GCD[i, (2*(2*n + 1) - i)*k]]}], {i, 2*(2*n + 1)}]); (* Array: *) Grid[Table[a[k, n], {k, 6}, {n, 6}]] (* Or array antidiagonals flattened: *) Flatten[Table[a[k - n + 1, n], {k, 7}, {n, k}]] CROSSREFS Cf. A047996. Sequence in context: A181005 A289644 A094478 * A064738 A067825 A239417 Adjacent sequences:  A273087 A273088 A273089 * A273091 A273092 A273093 KEYWORD nonn,tabl AUTHOR L. Edson Jeffery, May 14 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 27 03:27 EST 2020. Contains 338677 sequences. (Running on oeis4.)