A239310 Numbers of the form A001700(n)*k, n>=1, k>=2.

6, 9, 12, 15, 18, 20, 21, 24, 27, 30, 33, 36, 39, 40, 42, 45, 48, 50, 51, 54, 57, 60, 63, 66, 69, 70, 72, 75, 78, 80, 81, 84, 87, 90, 93, 96, 99, 100, 102, 105, 108, 110, 111, 114, 117, 120, 123, 126, 129, 130, 132, 135, 138, 140, 141, 144, 147

Offset: 1

Author

Bob Selcoe, Mar 31 2016

Keywords

• nonn
• easy

Comments

Numbers that are central coefficients T(2k,k) k>=2 in (a,b)-Pascal triangles, where (a,b) represent boundary conditions; i.e., T(2k,k) = (a+b)*A001700(k-1).

Examples

			a(n)=50 appears because A001700(2)=10, so T(6,3)=50 in (1,4)- and (2,3)-Pascal triangles.
		

Crossrefs

Cf. A001700.

Cf. A007318 (Pascal's triangle), A029600 ((2,3)-Pascal triangle), A095666 ((1,4)-Pascal triangle).

Programs

PARI

is(n)=my(k=1,t=3); while(n>=2*t, if(n%t==0, return(1)); k++; t=binomial(2*k+1, k+1)); 0 \\ Charles R Greathouse IV, Apr 04 2016

Formula

a(n) ~ kn, where k = 2.441823902640895564.... (This constant exists since A001700 grows exponentially.) - Charles R Greathouse IV, Apr 04 2016