A221533 a(n) is the number of integers of the form binomial(4*n^2 - k - 2, k - 1) / k, k=3, 4, ... , 2*n^2 - 2, n >= 2.

1, 9, 18, 33, 57, 60, 84, 141, 147, 187, 245, 265, 330, 417, 421, 430, 551, 620, 683, 837, 791, 865, 1056, 1044, 1182, 1288, 1278, 1506, 1737, 1677, 1685, 1983, 2097, 2228, 2517, 2433, 2423, 2780, 2926, 3079, 3253, 3216, 3563, 3733, 3713, 3872, 4249, 4318

Offset

2,2

Links

Peter J. C. Moses, Table of n, a(n) for n = 2..301

Formula

If (2n-1, 2n+1) is a pair of twin primes, then a(n) = 2*n^2 - 2*n - 3.

Mathematica

Table[Count[Table[Binomial[4*n^2-k-2, k-1]/k, {k, 3, 2*n^2-2}], _Integer], {n, 2, 30}] (* Peter J. C. Moses, Aug 17 2013 *)

Crossrefs

Cf. A177501.

Sequence in context: A140089 A183444 A349417 * A139591 A191268 A109668

Adjacent sequences: A221530 A221531 A221532 * A221534 A221535 A221536

Keyword

nonn

Author

Vladimir Shevelev, Aug 17 2013

Extensions

More terms from Peter J. C. Moses, Aug 17 2013

Status

approved