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A105038 Nonnegative n such that 6*n^2 + 6*n + 1 is a square. 10
0, 4, 44, 440, 4360, 43164, 427284, 4229680, 41869520, 414465524, 4102785724, 40613391720, 402031131480, 3979697923084, 39394948099364, 389969783070560, 3860302882606240, 38213059042991844, 378270287547312204, 3744489816430130200, 37066627876753989800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (I).

Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (II).

Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (III).

Editors, L'Intermédiaire des Mathématiciens, Query 4500: The equation x(x+1)/2 = y*(y+1)/3, L'Intermédiaire des Mathématiciens, 22 (1915), 255-260 (IV).

Index entries for linear recurrences with constant coefficients, signature (11,-11,1).

FORMULA

G.f.: 4*x/(1-11*x+11*x^2-x^3).

a(0)=0, a(1)=4, a(2)=44, a(n)=11*a(n-1)-11*a(n-2)+a(n-3). - Harvey P. Dale, Sep 29 2013

a(n) = (-6-(5-2*sqrt(6))^n*(-3+sqrt(6))+(3+sqrt(6))*(5+2*sqrt(6))^n)/12. - Colin Barker, Mar 05 2016

a(n) = (A072256(n+1) - 1)/2.

MATHEMATICA

CoefficientList[Series[4x/(1-11x+11x^2-x^3), {x, 0, 30}], x] (* or *) LinearRecurrence[{11, -11, 1}, {0, 4, 44}, 30] (* Harvey P. Dale, Sep 29 2013 *)

PROG

(PARI) for(n=0, 427284, if(issquare(6*n*(n+1)+1), print1(n, ", ")))

(PARI) Vec(4*x/(1-11*x+11*x^2-x^3)+O(x^99)) \\ Charles R Greathouse IV, Nov 13 2012

CROSSREFS

Cf. A001652, A001570, A049629, A105040, A104240, A077288, A105036, A103200, A105037.

Sequence in context: A187870 A216272 A221405 * A002278 A112897 A163013

Adjacent sequences:  A105035 A105036 A105037 * A105039 A105040 A105041

KEYWORD

nonn,easy

AUTHOR

Gerald McGarvey, Apr 03 2005

EXTENSIONS

More terms from Vladeta Jovovic, Apr 05 2005

Incorrect conjectures deleted by N. J. A. Sloane, Nov 24 2010

STATUS

approved

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Last modified July 2 12:39 EDT 2022. Contains 355004 sequences. (Running on oeis4.)