A091627 -id:A091627 - cp's OEIS frontend

0, 1, 3, 5, 7, 10, 12, 15, 18, 21, 24, 28, 30, 34, 38, 41, 44, 49, 51, 56, 60, 63, 67, 72, 75, 79, 83, 88, 91, 97, 99, 104, 109, 112, 117, 123, 125, 130, 135, 140, 143, 149, 152, 157, 163, 167, 170, 177, 180, 186, 190, 194, 199, 205, 209, 215, 219, 223

Offset: 1

Clark Kimberling, Apr 06 2012

nonn

Guide to related sequences:

A056924 ... 1<=x

A211159 ... 1<=x

A211261 ... 1<=x

A211262 ... 1<=x

A211263 ... 1<=x

A211264 ... 1<=x

A211265 ... 1<=x

A211266 ... 1<=x

A211267 ... 1<=x

A181972 ... 1<=x

A038548 ... 1<=x<=y<=n ... x*y=n

A072670 ... 1<=x<=y<=n ... x*y=n+1

A211270 ... 1<=x<=y<=n ... x*y=2n

A211271 ... 1<=x<=y<=n ... x*y=3n

A211272 ... 1<=x<=y<=n ... x*y=floor(n/2)

A094820 ... 1<=x<=y<=n ... x*y<=n

A091627 ... 1<=x<=y<=n ... x*y<=n+1

A211273 ... 1<=x<=y<=n ... x*y<=2n

A211274 ... 1<=x<=y<=n ... x*y<=3n

A211275 ... 1<=x<=y<=n ... x*y<=floor(n/2)

			a(6) counts these pairs: (1,2), (1,3), (1,4), (1,5), (1,6), (2,3), (2,4), (2,5), (2,6), (3,4).

Cf. A211261, A211264.

a = 1; b = n; z1 = 120;
t[n_] := t[n] = Flatten[Table[x*y, {x, a, b - 1},
{y, x + 1, b}]]
c[n_, k_] := c[n, k] = Count[t[n], k]
Table[c[n, n], {n, 1, z1}]           (* A056924 *)
Table[c[n, n + 1], {n, 1, z1}]       (* A211159 *)
Table[c[n, 2*n], {n, 1, z1}]         (* A211261 *)
Table[c[n, 3*n], {n, 1, z1}]         (* A211262 *)
Table[c[n, Floor[n/2]], {n, 1, z1}]  (* A211263 *)
Print
c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, a, m}]
Table[c1[n, n], {n, 1, z1}]          (* A211264 *)
Table[c1[n, n + 1], {n, 1, z1}]      (* A211265 *)
Table[c1[n, 2*n], {n, 1, z1}]        (* A211266 *)
Table[c1[n, 3*n], {n, 1, z1}]        (* A211267 *)
Table[c1[n, Floor[n/2]], {n, 1, z1}] (* A181972 *)

A211270 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y = 2n.

Original entry on oeis.org

0, 1, 1, 1, 1, 2, 1, 2, 2, 2, 1, 3, 1, 2, 3, 2, 1, 4, 1, 3, 3, 2, 1, 4, 2, 2, 3, 3, 1, 5, 1, 3, 3, 2, 3, 5, 1, 2, 3, 4, 1, 5, 1, 3, 5, 2, 1, 5, 2, 4, 3, 3, 1, 5, 3, 4, 3, 2, 1, 7, 1, 2, 5, 3, 3, 5, 1, 3, 3, 5, 1, 7, 1, 2, 5, 3, 3, 5, 1, 5, 4, 2, 1, 7, 3, 2, 3, 4, 1, 8, 3, 3, 3, 2, 3, 6, 1, 4, 5

Offset: 1

Clark Kimberling, Apr 07 2012

nonn

For a guide to related sequences, see A211266.

			a(12) counts these pairs: (2,12), (3,8), (4,6).
For n = 2, only the pair (2,2) satisfies the condition, thus a(2) = 1. - _Antti Karttunen_, Sep 30 2018

Antti Karttunen, Table of n, a(n) for n = 1..65537
David J. Hemmer and Karlee J. Westrem, Palindrome Partitions and the Calkin-Wilf Tree, arXiv:2402.02250 [math.CO], 2024. See Theorem 4.2 p. 7.

Cf. A000005, A211266, A211261.

seq(floor((numtheory:-tau(2*n)-1)/2),n=1..100); # Robert Israel, Feb 25 2019

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}]         (* this sequence *)
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}]
Print
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 *)

A211270(n) = sumdiv(2*n,y,(((2*n/y)<=y)&&(y<=n))); \\ Antti Karttunen, Sep 30 2018

a(n) = floor((A000005(2n)-1)/2). - Robert Israel, Feb 25 2019

Term a(2) corrected by Antti Karttunen, Sep 30 2018

A211271 Number of integer pairs (x,y) such that 0

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 1, 2, 1, 2, 1, 3, 1, 2, 2, 3, 1, 2, 1, 4, 2, 2, 1, 4, 2, 2, 2, 4, 1, 4, 1, 4, 2, 2, 3, 4, 1, 2, 2, 6, 1, 4, 1, 4, 3, 2, 1, 6, 2, 4, 2, 4, 1, 3, 3, 6, 2, 2, 1, 7, 1, 2, 3, 5, 3, 4, 1, 4, 2, 6, 1, 6, 1, 2, 4, 4, 3, 4, 1, 8, 2, 2, 1, 7, 3, 2, 2, 6, 1, 6, 3, 4, 2, 2, 3, 7, 1, 4, 3, 7, 1, 4, 1, 6, 5, 2, 1, 6

Offset: 1

Clark Kimberling, Apr 07 2012

nonn

For a guide to related sequences, see A211266.

			a(3) counts this pair: (3,3). - _Antti Karttunen_, Jan 15 2025
a(20) counts these pairs: (3,20), (4,15), (5,12), (6,10).

Antti Karttunen, Table of n, a(n) for n = 1..20000

Cf. A211266.

Cf. also A211262.

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}]
Print
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 *)

A211271(n) = { my(n3=3*n); sumdiv(n3,d,(d <= (n3/d) && (n3/d) <= n)); }; \\ Antti Karttunen, Jan 15 2025

Data section extended up to a(108) and a(3) corrected from 0 to 1 by Antti Karttunen, Jan 15 2025

A091626 Number of ordered integer pairs (b,c) with 0 <= b, c <= n such that both roots of x^2+bx+c=0 are integers.

Original entry on oeis.org

1, 2, 4, 6, 9, 11, 14, 16, 19, 22, 25, 27, 31, 33, 36, 39, 43, 45, 49, 51, 55, 58, 61, 63, 68, 71, 74, 77, 81, 83, 88, 90, 94, 97, 100, 103, 109, 111, 114, 117, 122, 124, 129, 131, 135, 139, 142, 144, 150, 153, 157, 160, 164, 166, 171, 174, 179, 182, 185, 187

Offset: 0

Eric W. Weisstein, Jan 24 2004

nonn

Also number of ordered pairs of nonnegative integers (i, j) such that i+j <= n and i*j <= n. - Seiichi Manyama, Sep 04 2021

			The six quadratics for a(3)=6 and their roots are as follows:
x^2 + 0*x + 0; x=0.
x^2 + 1*x + 0; x=0, x=-1.
x^2 + 2*x + 0; x=0, x=-2.
x^2 + 2*x + 1; x=-1.
x^2 + 3*x + 0; x=0, x=-3.
x^2 + 3*x + 2; x=-1, x=-2.

Griffin N. Macris, Table of n, a(n) for n = 0..9999
Eric Weisstein's World of Mathematics, Quadratic Equation

Cf. A000005, A006218, A038548, A067274, A091627.

a[n_] := a[n] = a[n-1] + Ceiling[ DivisorSigma[0, n]/2] + 1; a[0]=1; a[1]=2; Table[a[n], {n, 0, 59}] (* Jean-François Alcover, Nov 08 2012, after Vladeta Jovovic *)

a(n) = sum(i=0, n, sum(j=i, n-i, i*j<=n)); \\ Seiichi Manyama, Sep 04 2021

from math import isqrt
def A091626(n):
    m = isqrt(n)
    return 1 if n == 0 else n+sum(n//k for k in range(1, m+1))-m*(m-1)//2 # Chai Wah Wu, Oct 07 2021

a(n) = a(n-1) + ceiling(tau(n)/2) + 1, n>1. - Vladeta Jovovic, Jun 12 2004

a(n) = n + floor(sqrt(n))/2 + A006218(n)/2, n>0. - Griffin N. Macris, Jun 14 2016

A211272 Number of integer pairs (x,y) such that 0

Original entry on oeis.org

0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 3, 3, 1, 1, 2, 2, 2, 2, 3, 3, 1, 1, 3, 3, 1, 1, 3, 3, 2, 2, 2, 2, 1, 1, 4, 4, 2, 2, 2, 2, 2, 2, 3, 3, 1, 1, 4, 4, 1, 1, 3, 3, 2, 2, 2, 2, 2, 2, 5, 5, 1, 1, 2, 2, 2, 2, 4, 4, 1, 1, 4, 4, 1, 1, 3, 3, 3, 3, 2, 2, 1, 1, 5, 5, 2, 2

Offset: 1

Clark Kimberling, Apr 07 2012

nonn

For a guide to related sequences, see A211266.

			a(24) counts these pairs: (1,12), (2,6), (3,4).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A000005, A211266.

[0] cat [Ceiling(#Divisors( Floor(n/2))/2):n in [2..100]]; // Marius A. Burtea, Feb 07 2020

[seq(ceil(numtheory:-tau(floor(n/2))/2),n=1..100)]; - Robert Israel, Feb 07 2020

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}]
Print
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 *)

a(n) = ceiling(A000005(floor(n/2))/2). - Robert Israel, Feb 07 2020

A211273 Number of integer pairs (x,y) such that 0

Original entry on oeis.org

1, 3, 5, 7, 10, 13, 15, 19, 22, 25, 28, 32, 35, 39, 43, 46, 49, 55, 57, 62, 66, 69, 73, 78, 82, 86, 90, 95, 98, 104, 106, 112, 117, 120, 125, 131, 133, 138, 143, 148, 152, 158, 161, 166, 172, 176, 179, 186, 189, 196, 200, 204, 209, 215, 219, 225, 229, 233

Offset: 1

Clark Kimberling, Apr 07 2012

nonn

For a guide to related sequences, see A211266.

			a(5) counts these pairs: (1,1), (1,2), (1,3), (1,4), (1,5), (2,2), (2,3), (2,4), (2,5), (3,3)

Cf. A211266.

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}]
Print
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 *)

a(1)-a(2) corrected by Sean A. Irvine, Jan 22 2025

A211274 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= 3n.

Original entry on oeis.org

1, 3, 6, 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

Offset: 1

Clark Kimberling, Apr 07 2012

nonn

For a guide to related sequences, see A211266.

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

Cf. A211266.

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}]
Print
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 *)

a(1)-a(3) corrected by Sean A. Irvine, Jan 22 2025

A211275 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= floor(n/2).

Original entry on oeis.org

0, 1, 1, 2, 2, 3, 3, 5, 5, 6, 6, 8, 8, 9, 9, 11, 11, 13, 13, 15, 15, 16, 16, 19, 19, 20, 20, 22, 22, 24, 24, 27, 27, 28, 28, 31, 31, 32, 32, 35, 35, 37, 37, 39, 39, 40, 40, 44, 44, 46, 46, 48, 48, 50, 50, 53, 53, 54, 54, 58, 58, 59, 59, 62, 62, 64, 64, 66, 66, 68, 68

Offset: 1

Clark Kimberling, Apr 07 2012

nonn

For a guide to related sequences, see A211266.

Cf. A211266.

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}]
Print
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 *)

A379597 a(n) is the number of distinct solution sets to the quadratic equations ux^2 + vx + w = 0 with integer coefficients u, v, w, abs(u) + abs(v) + abs(w) <= n having a nonnegative discriminant.

Original entry on oeis.org

1, 4, 12, 24, 50, 80, 134, 192, 276, 366, 510, 632, 834, 1018, 1262, 1502, 1858, 2136, 2584, 2956, 3448, 3910, 4576, 5076, 5834, 6488, 7320, 8066, 9136, 9892, 11118, 12114, 13358, 14482, 15978, 17108, 18862, 20272, 22024, 23532, 25700, 27216, 29600, 31486, 33746

Offset: 1

Felix Huber, Feb 18 2025

nonn

Quadratic equations u*x^2 + v*x + w = 0 with real coefficients u, v, w and nonnegative discriminant v^2 - 4*u*w have two real solutions.

a(n) is even for n >= 2.

			a(3) = 12 because there are 12 equations with abs(u) + abs(v) + abs(w) <= 3 and distinct solution set having a nonnegative discriminant: (u, v, w) = (1, 0, 0), (1, -1, 0), (1, 1, 0), (1, 0, -1), (1, -1, -1), (1, 1, -1), (1, -2, 0), (1, 2, 0), (1, 0, -2), (2, -1, 0), (2, 1, 0), and (2, 0, -1). Multiplied equations like 2*(1, 0, 0) = (2, 0, 0) or (-1)*(1, -1, 0) = (-1, 1, 0) do not have a distinct solution set.

Felix Huber, Table of n, a(n) for n = 1..3800
Eric Weisstein's World of Mathematics, Quadratic Equation

Cf. A067274, A091626, A091627, A364384, A364385, A365876, A365877, A381710, A381711.

A379597:=proc(n)
   option remember;
   local a,u,v,w;
   if n=1 then
      1
   else
      a:=0;	
      for u to n-1 do
         for v from 0 to n-u do
            w:=n-u-v;
            if igcd(u,v,w)=1 then
               if v=0 then
                  a:=a+1
               elif w=0 or w>=v^2/(4*u) then
                  a:=a+2
               else
                  a:=a+4
               fi
            fi
         od
      od;
      a+procname(n-1)
   fi;
end proc;
seq(A379597(n),n=1..45);

A381710 a(n) is the number of distinct solution sets to the quadratic equations ux^2 + vx + w = 0 with integer coefficients u, v, w, abs(u) + abs(v) + abs(w) <= n having a negative discriminant.

Original entry on oeis.org

0, 1, 5, 11, 25, 39, 69, 99, 143, 189, 265, 327, 437, 529, 653, 777, 965, 1107, 1343, 1531, 1783, 2021, 2367, 2619, 3013, 3343, 3771, 4153, 4707, 5087, 5721, 6229, 6865, 7437, 8197, 8767, 9677, 10391, 11279, 12043, 13155, 13919, 15147, 16101, 17249, 18301, 19763

Offset: 1

Felix Huber, Mar 06 2025

nonn

Quadratic equations u*x^2 + v*x + w = 0 with real coefficients u, v, w and negative discriminant v^2 - 4*u*w have two complex solutions.

a(n) is odd for n >= 2.

			a(3) = 5 because there are 5 equations with abs(u) + abs(v) + abs(w) <= 3 and distinct solution set having a negative discriminant: (u, v, w) = (1, 0, 1), (1, -1, 1), (1, 1, 1), (1, 0, 2), (2, 0, 1). Multiplied equations like (-1)*(1, -1, 1) = (-1, 1, -1) do not have a distinct solution set.

Felix Huber, Table of n, a(n) for n = 1..5000
Eric Weisstein's World of Mathematics, Quadratic Equation

Cf. A067274, A091626, A091627, A364384, A364385, A365876, A365877, A379597, A381711.

A381710:=proc(n)
   option remember;
   local a,u,v,w;
      if n=1 then
      0
   else
      a:=0;
      for u to n-1 do
         for v from 0 to n-u do
            w:=n-u-v;
               if igcd(u,v,w)=1 then
                  if v=0 then
                     a:=a+1
                  elif w>v^2/(4*u) then
                    a:=a+2
               fi
            fi
         od
      od;
      a+procname(n-1)
   fi;
end proc;
seq(A381710(n),n=1..47);

Showing 1-10 of 11 results. Next

cp's OEIS Frontend

A211266 Number of integer pairs (x,y) such that 0

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A211270 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y = 2n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

Extensions

A211271 Number of integer pairs (x,y) such that 0

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A091626 Number of ordered integer pairs (b,c) with 0 <= b, c <= n such that both roots of x^2+bx+c=0 are integers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Python

Formula

A211272 Number of integer pairs (x,y) such that 0

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

Formula

A211273 Number of integer pairs (x,y) such that 0

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

Extensions

A211274 Number of integer pairs (x,y) such that 0 < x <= y <= n and x*y <= 3n.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

A379597 a(n) is the number of distinct solution sets to the quadratic equations ux^2 + vx + w = 0 with integer coefficients u, v, w, abs(u) + abs(v) + abs(w) <= n having a nonnegative discriminant.

A381710 a(n) is the number of distinct solution sets to the quadratic equations ux^2 + vx + w = 0 with integer coefficients u, v, w, abs(u) + abs(v) + abs(w) <= n having a negative discriminant.