A211274 - OEIS

A211274

Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= 3n.

0, 2, 5, 9, 12, 16, 20, 24, 28, 33, 37, 43, 46, 52, 57, 62, 67, 72, 78, 84, 88, 95, 99, 107, 111, 117, 124, 130, 134, 142, 147, 154, 159, 166, 173, 179, 184, 191, 197, 206, 210, 218, 223, 231, 237, 243, 250, 259, 264, 271, 277, 286, 289, 299, 305, 313

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OFFSET

1,2

COMMENTS

For a guide to related sequences, see A211266.

LINKS

Table of n, a(n) for n=1..56.

EXAMPLE

a(4) counts these pairs: (1,1), (1,2), (1,3), (1,4), (2,3), (2,4), (3,3,), (3,4), (4,4).

MATHEMATICA

a = 1; b = n; z1 = 120;

t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},

{y, x, b}]]

c[n_, k_] := c[n, k] = Count[t[n], k]

Table[c[n, n], {n, 1, z1}] (* A038548 *)

Table[c[n, n + 1], {n, 1, z1}] (* A072670 *)

Table[c[n, 2*n], {n, 1, z1}] (* A211270 *)

Table[c[n, 3*n], {n, 1, z1}] (* A211271 *)

Table[c[n, Floor[n/2]], {n, 1, z1}] (* A211272 *)

c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]

Table[c1[n, n], {n, 1, z1}] (* A094820 *)

Table[c1[n, n + 1], {n, 1, z1}] (* A091627 *)

Table[c1[n, 2*n], {n, 1, z1}] (* A211273 *)

Table[c1[n, 3*n], {n, 1, z1}] (* A211274 *)

Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A211275 *)

CROSSREFS

Cf. A211266.

Sequence in context: A047385 A284624 A086814 * A276217 A354835 A086343

Adjacent sequences: A211271 A211272 A211273 * A211275 A211276 A211277

KEYWORD

nonn

AUTHOR

Clark Kimberling, Apr 07 2012

STATUS

approved