cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

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

Original entry on oeis.org

62, 1532, 50830, 1855110, 71292624, 2833906726, 115381823442, 4782782748036, 201037496481198, 8545008347772070, 366526239773992472, 15841416797530328062, 689082764185943820494, 30139654907867753730956, 1324572400153686602854414, 58455392031254908270140098
Offset: 1

Views

Author

N. J. A. Sloane, Dec 15 2017

Keywords

Links

Crossrefs

Cf. A241926, A296360, A296361, A296362.

Programs

  • 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 *)
  • 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

Formula

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

Extensions

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

A296360 Number of monohedral disk tilings of type C^t_{2n+1,3}.

Original entry on oeis.org

116, 6402, 446930, 34121322, 2741227176, 227759341712, 19382568941318, 1679333068357460, 147541888215426742, 13107891004266127974, 1175188298096727647322, 106164291028322202227232, 9652457243380891557169712, 882443342536355491502025678
Offset: 1

Views

Author

N. J. A. Sloane, Dec 15 2017

Keywords

Links

Crossrefs

Cf. A241926, A296359, A296361, A296362.

Programs

  • Mathematica
    U[n_, k_] := DivisorSum[GCD[n, k], EulerPhi[#]*Binomial[(n + k)/#, n/#]/(n + k) &];
a[n_] := 2*Sum[U[i, 3*(4*n + 2 - i)], {i, 0, 4*n + 2}];
Array[a, 16] (* Jean-François Alcover, Jun 14 2018, after Andrew Howroyd *)
  • 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,3*(4*n+2-i)))} \\ Andrew Howroyd, Jan 09 2018

Formula

a(n) = 2*Sum_{i=0..4*n+2} A241926(i, 3*(4*n+2-i)). - Andrew Howroyd, Jan 09 2018

Extensions

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

A296361 Number of monohedral disk tilings of type C^t_{3,n}.

Original entry on oeis.org

2, 62, 116, 200, 318, 476, 682, 946, 1272, 1674, 2152, 2724, 3394, 4176, 5078, 6110, 7284, 8614, 10108, 11784, 13646, 15716, 18002, 20522, 23288, 26314, 29616, 33212, 37114, 41344, 45910, 50838, 56140, 61838, 67948, 74488, 81478, 88940, 96890, 105354, 114344
Offset: 1

Views

Author

N. J. A. Sloane, Dec 15 2017

Keywords

Links

Crossrefs

Cf. A241926, A296359, A296360, A296362.

Programs

  • 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*(6 - i)], {i, 0, 6}];
Array[a, 50] (* Jean-François Alcover, Jun 14 2018, after Andrew Howroyd *)
  • 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, 6, U(i,n*(6-i))))} \\ Andrew Howroyd, Jan 09 2018

Formula

Conjectures from Colin Barker, Jan 09 2018: (Start)
G.f.: 2*x*(1 + 28*x - 33*x^2 - 10*x^3 + 34*x^4 - 16*x^5 - 26*x^6 + 35*x^7 + 8*x^8 - 32*x^9 + 13*x^10) / ((1 - x)^5*(1 + x)*(1 + x + x^2 + x^3 + x^4)).
a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - 3*a(n-6) + 2*a(n-7) + 2*a(n-8) - 3*a(n-9) + a(n-10) for n>11.
(End)
a(n) = 2*Sum_{i=0..6} A241926(i, n*(6-i)) for n > 1. - Andrew Howroyd, Jan 09 2018

Extensions

Terms a(6) and beyond from Lars Blomberg, Jan 09 2018
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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