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A024352 Numbers which are the difference of two positive squares, c^2 - b^2 with 1 <= b < c. 18
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 (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 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

T. D. Noe, Table of n, a(n) for n = 1..1000

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.: (-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(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 *)

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

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

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Last modified September 26 01:25 EDT 2017. Contains 292500 sequences.