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

1,4

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.

Links

Table of n, a(n) for n=1..63.

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A003016, A007318.

Sequence in context: A306683 A184586 A190511 * A033035 A047390 A184653

Adjacent sequences: A260463 A260464 A260465 * A260467 A260468 A260469

Keyword

nonn

Author

Alex Jordan, Jul 26 2015

Extensions

More terms from Michel Marcus, Jul 30 2015

Status

approved