OFFSET
1,1
COMMENTS
Numbers a such that a*(a+1) = c2 - b2 with b <= a < c let a(1)=3 then a(2*n) = a(2*n-1) + 1 and a(2*n+1) = a(2*n) + 3. [Pierre CAMI, Jan 15 2009]
LINKS
FORMULA
a(1)=4; thereafter a(2*n) = a(2*n-1) + 3, a(2*n+1) = a(2*n) + 1.
a(n) = 4*n - a(n-1) - 1 (with a(1)=3). [Vincenzo Librandi, Nov 26 2010]
From Colin Barker, Mar 06 2013: (Start)
a(n) = (1 - (-1)^n + 4*n)/2.
a(n) = a(n-1) + a(n-2) - a(n-3).
G.f.: x*(x+3) / ((x-1)^2*(x+1)). (End)
EXAMPLE
4*5 + 4*4 = 6*6; 7*8 + 5*5 = 9*9; 8*9 + 7*7 = 11*11;
3*4 = 4*4 - 2*2; a(1)=3; 4*5 = 6*6 - 4*4; a(2) = 4; 7*6 = 9*9 - 5*5; a(3)=7. [Pierre CAMI, Jan 15 2009]
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {3, 4, 7}, 70] (* Harvey P. Dale, Jan 07 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Pierre CAMI, Jan 14 2009, Jan 15 2009
EXTENSIONS
More terms from Vincenzo Librandi, Nov 26 2010
STATUS
approved