OFFSET
0,2
COMMENTS
It may be seen that the terms of the (signed) sequence consist of a subset of the odd squares minus two.
One leg of Pythagorean triangles with hypotenuse a square: a(n)^2 + A069074(n-1)^2 = A007204(n)^2. - Martin Renner, Nov 12 2011
REFERENCES
Albert H. Beiler, Recreations in the theory of numbers, New York: Dover, 2nd ed., 1966, p. 106, table 53.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 4*b(n)^2 - 4*b(n) - 1 where b(n) = n-th pronic number A002378(n).
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=-1, a(1)=7, a(2)=119, a(3)=527, a(4)=1519. - Harvey P. Dale, Oct 20 2011
G.f.: (x*(x*((x-12)*x-74)-12)+1)/(x-1)^5. - Harvey P. Dale, Oct 20 2011
Sum_{n>=0} 1/a(n) = cot(Pi/sqrt(2))*Pi/(2*sqrt(2)). - Amiram Eldar, Jan 22 2024
MATHEMATICA
Table[4n^4+8n^3-4n-1, {n, 0, 40}] (* Harvey P. Dale, Oct 20 2011 *)
PROG
(PARI) a(n)=(2*n^2-1)*(2*n^2+4*n+1) \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Stuart M. Ellerstein (ellerstein(AT)aol.com), Nov 01 2000
EXTENSIONS
More terms from James A. Sellers, Nov 02 2000
STATUS
approved