OFFSET
1,1
COMMENTS
These are the solutions to the equation x^2 + xy = n where y mod 2 = 0, y is positive and x is any positive integer. - Andrew S. Plewe, Oct 19 2007
Ordered different terms of A120070 = 3, 8, 5, 15, 12, 7, ... (which contains two 15's, two 40's, and two 48's). Complement: A139544. (See A139491.) - Paul Curtz, Sep 01 2009
A024359(a(n)) > 0. - Reinhard Zumkeller, Nov 09 2012
If a(n) mod 6 = 3, n > 1, then a(n) = c^2 - f(a(n))^2 where f(n) = (floor(4*n/3) - 3 - n)/2. For example, 171 = 30^2 - 27^2 and f(171) = 27. - Gary Detlefs, Jul 15 2014
LINKS
Ray Chandler, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. Noe)
Ron Knott, Pythagorean Triples and Online Calculators
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).
FORMULA
Consists of all positive integers except 1, 4 and numbers == 2 (mod 4).
a(n) = a(n-3) + 4, n > 4.
G.f.: (3 + 2*x + 2*x^2 - 2*x^3 - x^4)/(1 - x - x^3 + x^4). - Ralf Stephan, before May 13 2008
a(n) = a(n-1) + a(n-3) - a(n-4), for n > 5. - Ant King, Oct 03 2011
a(n) = 4 + floor((4*n-3)/3), n > 1. - Gary Detlefs, Jul 15 2014
MATHEMATICA
Union[Flatten[Table[Select[Table[b^2 - c^2, {c, b-1}], # < 100 &], {b, 100}]]] (* Robert G. Wilson v, Jun 05 2004 *)
LinearRecurrence[{1, 0, 1, -1}, {3, 5, 7, 8, 9}, 70] (* Harvey P. Dale, Dec 20 2021 *)
PROG
(Haskell)
a024352 n = a024352_list !! (n-1)
a024352_list = 3 : drop 4 a042965_list
-- Reinhard Zumkeller, Nov 09 2012
(PARI) is(n)=(n%4!=2 && n>4) || n==3 \\ Charles R Greathouse IV, May 31 2013
(Magma) [3] cat [4 +Floor((4*n-3)/3): n in [2..100]]; // G. C. Greubel, Apr 22 2023
(SageMath)
def A024352(n): return 4 + ((4*n-3)//3) - int(n==1)
[A024352(n) for n in range(1, 101)] # G. C. Greubel, Apr 22 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
Edited by N. J. A. Sloane, Sep 19 2008
STATUS
approved