

A260466


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


0



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
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OFFSET

1,4


COMMENTS

Ignoring the first two terms of A003016, a(n) is partial sums of A003016.
a(n) >= 2n5 trivially; for n>=7, a(n) > 2n5.


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



