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A161483 Positive numbers y such that y^2 is of the form x^2+(x+151)^2 with integer x. 3
109, 151, 265, 389, 755, 1481, 2225, 4379, 8621, 12961, 25519, 50245, 75541, 148735, 292849, 440285, 866891, 1706849, 2566169, 5052611, 9948245, 14956729, 29448775, 57982621, 87174205, 171640039, 337947481, 508088501, 1000391459, 1969702265 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

(-60, a(1)) and (A161482(n), a(n+1)) are solutions (x, y) to the Diophantine equation x^2+(x+151)^2 = y^2.

lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).

lim_{n -> infinity} a(n)/a(n-1) = (187+78*sqrt(2))/151 for n mod 3 = {0, 2}.

lim_{n -> infinity} a(n)/a(n-1) = (24723+6758*sqrt(2))/151^2 for n mod 3 = 1.

LINKS

Table of n, a(n) for n=1..30.

FORMULA

a(n) = 6*a(n-3)-a(n-6) for n > 6; a(1)=109, a(2)=151, a(3)=265, a(4)=389, a(5)=755, a(6)=1481.

G.f.: (1-x)*(109+260*x+525*x^2+260*x^3+109*x^4) / (1-6*x^3+x^6).

a(3*k-1) = 151*A001653(k) for k >= 1.

EXAMPLE

(-60, a(1)) = (-60, 109) is a solution: (-60)^2+(-60+151)^2 = 3600+8281 = 11881 = 109^2.

(A161482(1), a(2)) = (0, 151) is a solution: 0^2+(0+151)^2 = 22801 = 151^2.

(A161482(3), a(4)) = (189, 389) is a solution: 189^2+(189+151)^2 = 35721+115600 = 151321 = 389^2.

PROG

(PARI) {forstep(n=-60, 100000000, [1, 3], if(issquare(2*n^2+302*n+22801, &k), print1(k, ", ")))}

CROSSREFS

Cf. A161482, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A161484 (decimal expansion of (187+78*sqrt(2))/151), A161485 (decimal expansion of (24723+6758*sqrt(2))/151^2).

Sequence in context: A325074 A182476 A182451 * A283792 A333743 A141948

Adjacent sequences:  A161480 A161481 A161482 * A161484 A161485 A161486

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Jun 13 2009

STATUS

approved

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Last modified May 13 16:56 EDT 2021. Contains 343862 sequences. (Running on oeis4.)