A260466 Number of integers in Pascal's triangle strictly between 1 and n.

0, 0, 1, 3, 5, 7, 10, 12, 14, 16, 20, 22, 24, 26, 28, 32, 34, 36, 38, 40, 43, 47, 49, 51, 53, 55, 57, 59, 63, 65, 67, 69, 71, 73, 75, 79, 83, 85, 87, 89, 91, 93, 95, 97, 99, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 125, 129, 131, 133, 135, 137, 139, 141

Offset: 1

Author

Alex Jordan, Jul 26 2015

Keywords

• nonn

Comments

Ignoring the first two terms of A003016, a(n) is partial sums of A003016.

a(n) >= 2n-5 trivially; for n>=7, a(n) > 2n-5.

Examples

			For n=7, the members of Pascal's triangle strictly between 1 and 7 are C(2,1), C(3,1), C(3,2), C(4,1), C(4,2), C(4,3), C(5,1), C(5,4), C(6,1), and C(6,5). So a(7)=10.
		

Crossrefs

Cf. A003016, A007318.

Programs

Mathematica

t = 0 * Range[101]; Do[x = Binomial[a, b]; If[1 < x <= 100, t[[x + 1]]++], {a, 100}, {b, a}]; Accumulate@ t (* Giovanni Resta, Aug 16 2015 *)

PARI

nbn(n) = {my(nb = 0); for (j=1, n, for (k=1, n, b = binomial(j, k); if ((b>1) && (b<=n), nb++););); nb;} \\ Michel Marcus, Jul 30 2015

Extensions

More terms from Michel Marcus, Jul 30 2015