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A059403 Quarter-squared applied twice. 2
0, 0, 0, 1, 4, 9, 20, 36, 64, 100, 156, 225, 324, 441, 600, 784, 1024, 1296, 1640, 2025, 2500, 3025, 3660, 4356, 5184, 6084, 7140, 8281, 9604, 11025, 12656, 14400, 16384, 18496, 20880, 23409, 26244, 29241, 32580, 36100, 40000, 44100, 48620, 53361 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000 (first 501 terms from Harry J. Smith)

Index entries for linear recurrences with constant coefficients, signature (2, 1, -4, 2, 0, -2, 4, -1, -2, 1).

FORMULA

a(n) = floor(floor(n^2/4)^2/4) = A002620(A002620(n))).

a(4n) = 4n^4; a(4n+1) = n^2*(2n+1)^2;

a(4n+2) = 2n(n+1)(2n(n+1)+1); a(4n+3) = (n+1)^2*(2n+1)^2.

a(2n) = A060494(2n); a(2n-1) = A060494(2n-1)-A011861(n).

G.f.: x^3(1+2x+2x^3+x^4)/((1-x)^5*(1+x)^3*(1+x^2)). [R. J. Mathar, Sep 09 2008]

EXAMPLE

a(9)=100 since the ninth quarter-square is 20 and the twentieth quarter-square is 100.

MATHEMATICA

Floor[Floor[Range[0, 50]^2/4]^2/4] (* or *) LinearRecurrence[{2, 1, -4, 2, 0, -2, 4, -1, -2, 1}, {0, 0, 0, 1, 4, 9, 20, 36, 64, 100}, 50] (* Harvey P. Dale, Dec 13 2014 *)

PROG

(PARI) { default(realprecision, 10); for (n = 0, 500, write("b059403.txt", n, " ", floor(floor(n^2/4)^2/4)); ) } \\ Harry J. Smith, Jun 26 2009

CROSSREFS

Cf. A008233 for an alternative approach.

Sequence in context: A256054 A164931 A066186 * A009909 A009910 A060494

Adjacent sequences:  A059400 A059401 A059402 * A059404 A059405 A059406

KEYWORD

easy,nonn

AUTHOR

Henry Bottomley, Mar 21 2001

STATUS

approved

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Last modified February 27 15:49 EST 2020. Contains 332307 sequences. (Running on oeis4.)