The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A330407

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A330407

Number of ordered integer pairs (b,c) with -n <= b <= n and -n <= c <= n such that both roots of x^2 + b*x + c = 0 are distinct integers.
(history; published version)

#28 by Alois P. Heinz at Thu Jan 30 17:45:54 EST 2020

STATUS

reviewed

approved

#27 by Hugo Pfoertner at Thu Jan 30 13:33:11 EST 2020

STATUS

proposed

reviewed

#26 by Michel Marcus at Thu Jan 30 13:23:06 EST 2020

STATUS

editing

proposed

#25 by Michel Marcus at Thu Jan 30 13:22:06 EST 2020

DATA

0, 3, 7, 13, 20, 26, 36, 42, 52, 59, 69, 75, 89, 95, 105, 115, 126, 132, 146, 152, 166, 176, 186, 192, 210, 217, 227, 237, 251, 257, 275, 281, 295, 305, 315, 325, 344, 350, 360, 370, 388, 394, 412, 418, 432, 446, 456, 462, 484, 491, 505, 515, 529, 535, 553, 563, 581

OFFSET

1,1

0,2

MATHEMATICA

ok[b_, c_] := Block[{d = b^2 - 4 c}, d > 0 && IntegerQ@ Sqrt@ d]; a[n_] := Sum[ Boole@ ok[b, c], {b, -n, n}, {c, -n, n}]; Array[a, 5057, 0] (* Giovanni Resta, Jan 28 2020 *)

PROG

(Python 3.7) [sum([1 for b in range(-n, n+1) for c in range(-n, n+1) if b**2-4*c > 0 and int((-b+(b**2-4*c)**0.5)/2) == (-b+(b**2-4*c)**0.5)/2]) for n in range(1, 0, 101)]

EXTENSIONS

a(0)=0 prepended by Michel Marcus, Jan 30 2020

STATUS

approved

editing

Discussion

Thu Jan 30

13:23

Michel Marcus: when n=0, x^2 has both roots 0, so not distinct , so a(0)=0

#24 by Giovanni Resta at Wed Jan 29 16:01:38 EST 2020

STATUS

reviewed

approved

#23 by Andrey Zabolotskiy at Wed Jan 29 12:24:31 EST 2020

STATUS

proposed

reviewed

#22 by Andrey Zabolotskiy at Wed Jan 29 12:24:28 EST 2020

STATUS

editing

proposed

#21 by Andrey Zabolotskiy at Wed Jan 29 12:24:19 EST 2020

FORMULA

a(n) = A067274(n) - A001650(n+1) for n > 1.

STATUS

proposed

editing

#20 by Michel Marcus at Tue Jan 28 13:22:57 EST 2020

STATUS

editing

proposed

#19 by Michel Marcus at Tue Jan 28 13:22:42 EST 2020

PROG

(PARI) isok(b, c) = my(q); (b^2 > 4*c) && issquare(b^2-4*c);

STATUS

proposed

editing