A273187 a(n) is the third number in a triple consisting of 3 numbers, which when squared are part of a right diagonal of magic square of squares.

99, 449, 2499, 14449, 84099, 490049, 2856099, 16646449, 97022499, 565488449, 3295908099, 19209960049, 111963852099, 652573152449, 3803475062499, 22168277222449, 129206188272099, 753068852410049, 4389206926188099, 25582172704718449, 149103829302122499

Offset

0,1

Links

Colin Barker, Table of n, a(n) for n = 0..1000

E. Gutierrez, Recursion Methods to Generate New Integer Sequences (Part VIF)

E. Gutierrez, Table of Tuples and Use of Magic Ratio for Tuple Conversion (Part IB)

E. Gutierrez, Table of Tuples for Square of Squares (Part IC)

Index entries for linear recurrences with constant coefficients, signature (7,-7,1).

Formula

a(0)= 99, a(1)= 449, a(n+1)= a(n)*6 - a(n-1) - k where k=96.

From Colin Barker, May 18 2016: (Start)

a(n) = (24+25/2*(3-2*sqrt(2))^(1+n)+25/2*(3+2*sqrt(2))^(1+n)).

a(n) = 7*a(n-1)-7*a(n-2)+a(n-3) for n>2.

G.f.: (99-244*x+49*x^2) / ((1-x)*(1-6*x+x^2)).

(End)

a(n) = 24 + 25*A001541(n+1). - R. J. Mathar, Jun 07 2016

Example

a(2)= 449*6 - (99 + 96)= 2499;
a(3)= 2499*6 - (449 + 96)= 14449.

Mathematica

CoefficientList[Series[(99 - 244 x + 49 x^2)/((1 - x) (1 - 6 x + x^2)), {x, 0, 20}], x] (* Michael De Vlieger, May 20 2016 *)

Prog

(PARI) Vec((99-244*x+49*x^2)/((1-x)*(1-6*x+x^2)) + O(x^50)) \\ Colin Barker, May 18 2016

Crossrefs

Cf. A273182, A273189.

Sequence in context: A304675 A316122 A157659 * A322830 A212779 A321636

Adjacent sequences: A273184 A273185 A273186 * A273188 A273189 A273190

Keyword

nonn,easy

Author

Eddie Gutierrez, May 17 2016

Status

approved