A082651 -id:A082651 - cp's OEIS frontend

A052454 Positive integer values of k such that 10*k^2 - 9 is a square.

1, 3, 13, 25, 111, 493, 949, 4215, 18721, 36037, 160059, 710905, 1368457, 6078027, 26995669, 51965329, 230804967, 1025124517, 1973314045, 8764510719, 38927735977, 74933968381, 332820602355, 1478228842609, 2845517484433, 12638418378771

Offset: 1

John W. Layman, May 20 2003

			25 is a term of the sequence since 10*25^2-9 = 6241 = 79^2.

Paolo Xausa, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,0,38,0,0,-1).

Cf. A077442, A082651, A221874.

LinearRecurrence[{0, 0, 38, 0, 0, -1}, {1, 3, 13, 25, 111, 493}, 50] (* Paolo Xausa, Mar 18 2024 *)

a(n) = 38*a(n-3)-a(n-6).

G.f.: x*(1-x)*(1+4*x+17*x^2+4*x^3+x^4)/(1-38*x^3+x^6). [Colin Barker, Jun 13 2012]

More terms from Bruno Berselli, Jan 29 2013

A281064 Values of x such that x^2 = 5*y^2 + 11, where x and y are positive integers.

Original entry on oeis.org

4, 16, 56, 284, 1004, 5096, 18016, 91444, 323284, 1640896, 5801096, 29444684, 104096444, 528363416, 1867934896, 9481096804, 33518731684, 170131379056, 601469235416, 3052883726204, 10792927505804, 54781775692616, 193671225869056, 983019078740884

Offset: 1

Colin Barker, Jan 14 2017

The corresponding values of y are in A082651.

			56 is in the sequence because 56^2 = 3136 = 5*25^2+11.

Colin Barker, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (0,18,0,-1).

Cf. A082651.

LinearRecurrence[{0,18,0,-1},{4,16,56,284},30] (* Harvey P. Dale, May 28 2020 *)

Vec(4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)) + O(x^30))

a(n) = ((-2-r)^n*(r-5) + (5+r)*(r-2)^n + (15+7*r)*(r+2)^n + (2-r)^n*(7*r-15)) / (4*r) where r=sqrt(5).
a(n) = 18*a(n-2) - a(n-4) for n>3.
G.f.: 4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)).

cp's OEIS Frontend

A052454 Positive integer values of k such that 10*k^2 - 9 is a square.

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