login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A296362 Number of monohedral disk tilings of type C^t_{5,n}. 4
2, 1532, 6402, 19884, 51128, 115188, 235180, 445096, 792822, 1343814, 2185396, 3431466, 5227806, 7758398, 11251894, 15989150, 22311572, 30630012, 41434474, 55305224, 72924016, 95086728, 122717140, 156881256, 198802766, 249880274, 311704608, 386077910 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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..10} A241926(i, n*(10-i)) for n > 1. - Andrew Howroyd, Jan 09 2018
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
MATHEMATICA
U[n_, k_] := DivisorSum[GCD[n, k], EulerPhi[#]*Binomial[(n+k)/#, n/#]/(n+k) &];
a[1] = 2; a[n_] := 2*Sum[ U[i, n*(10 - i)], {i, 0, 10}];
Array[a, 30] (* 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*if(n<2, n==1, sum(i=0, 10, U(i, n*(10-i))))} \\ Andrew Howroyd, Jan 09 2018
CROSSREFS
Sequence in context: A226699 A110027 A179866 * A282999 A201242 A062585
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 15 2017
EXTENSIONS
Terms a(6) and beyond from Lars Blomberg, Jan 09 2018
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)