A295130 a(n) = 3*n*(64*n^2 + 1).

195, 1542, 5193, 12300, 24015, 41490, 65877, 98328, 139995, 192030, 255585, 331812, 421863, 526890, 648045, 786480, 943347, 1119798, 1316985, 1536060, 1778175, 2044482, 2336133, 2654280, 3000075, 3374670, 3779217, 4214868, 4682775, 5184090, 5719965, 6291552, 6900003, 7546470, 8232105, 8958060, 9725487

Offset

1,1

References

Martin Gardner, Mathematical Carnival, 1975, Alfred A. Knopf Inc., New York.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Stuart Anderson, Squared squares, 2014

Michael H. Bischoff, Squares in a square

Wikipedia, Squaring the square

Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).

Formula

a(n) = 3*n*(64*n^2 + 1).

From Colin Barker, Nov 23 2017: (Start)

G.f.: 3*x*(65 + 254*x + 65*x^2) / (1 - x)^4.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

(End)

a(n) = A008585(n) * A158686(n). - Omar E. Pol, Nov 24 2017

E.g.f.: 3*x*e^x * (65 + 192*x + 64*x^2). - Iain Fox, Dec 22 2017

Example

For examples see "Squares in a square" in the LINKS section.

Mathematica

f[n_] := 3n (64n^2 +1); Array[f, 33] (* or *)
CoefficientList[ Series[(3 (65 +254x +65x^2))/(-1 +x)^4, {x, 0, 33}], x] (* or *)
LinearRecurrence[{4, -6, 4, -1}, {195, 1542, 5193, 12300}, 34] (* Robert G. Wilson v, Dec 27 2017 *)

Prog

(PARI) Vec(3*x*(65 + 254*x + 65*x^2) / (1 - x)^4 + O(x^40)) \\ Colin Barker, Nov 23 2017
(PARI) a(n) = 192*n^3 + 3*n \\ Iain Fox, Dec 22 2017

Crossrefs

Cf. A008585, A158686.

Sequence in context: A158003 A225713 A172354 * A257765 A259694 A066232

Adjacent sequences: A295127 A295128 A295129 * A295131 A295132 A295133

Keyword

nonn,easy

Author

Michael H. Bischoff, Nov 15 2017

Status

approved