

A024352


Numbers which are the difference of two positive squares, c^2  b^2 with 1 <= b < c.


21



3, 5, 7, 8, 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, 23, 24, 25, 27, 28, 29, 31, 32, 33, 35, 36, 37, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 52, 53, 55, 56, 57, 59, 60, 61, 63, 64, 65, 67, 68, 69, 71, 72, 73, 75, 76, 77, 79, 80, 81, 83, 84, 85, 87, 88, 89, 91, 92, 93, 95, 96
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

These are the solutions to the equation x^2 + xy = n where y mod 2 is zero, 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^2f(a(n))^2 where f(n) = (floor(4*n/3)3n)/2. For example, 171 = 30^227^2 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(n3) + 4, n>4.
G.f.: (x^4  2*x^3 + 2*x^2 + 2*x + 3)/(x^4  x^3  x + 1).  Ralf Stephan, before May 13 2008
a(n) = a(n1)+a(n3)a(n4), for n>5.  Ant King, Oct 03 2011
a(n) = 4 + floor((4*n3)/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 *)


PROG

(Haskell)
a024352 n = a024352_list !! (n1)
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


CROSSREFS

Same as A042965 except for initial terms.  Michael Somos, Jun 08 2000
Different from A020884.
Cf. A009005, A020884.
Sequence in context: A025051 A020884 A183855 * A288525 A134407 A218979
Adjacent sequences: A024349 A024350 A024351 * A024353 A024354 A024355


KEYWORD

nonn,easy


AUTHOR

David W. Wilson


EXTENSIONS

Edited by N. J. A. Sloane, Sep 19 2008


STATUS

approved



