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)
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
KEYWORD
nonn,easy
AUTHOR
Michael H. Bischoff, Nov 15 2017
STATUS
approved