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A000534 Numbers that are not the sum of 4 nonzero squares. 6
0, 1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41, 56, 96, 128, 224, 384, 512, 896, 1536, 2048, 3584, 6144, 8192, 14336, 24576, 32768, 57344, 98304, 131072, 229376, 393216, 524288, 917504, 1572864, 2097152, 3670016, 6291456, 8388608, 14680064 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

For n > 15, a(n) = A006431(n-1). - Thomas Ordowski, Nov 18 2012

REFERENCES

J. H. Conway, The Sensual (Quadratic) Form, M.A.A., 1997, p. 140.

E. Grosswald, Representations of Integers as Sums of Squares. Springer-Verlag, NY, 1985, Theorem 3, pp. 74-75.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..100

Pierre de la Harpe, Lagrange et la variation des théorèmes, Images des Mathématiques, CNRS, 2014.

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

Index entries for sequences related to sums of squares

FORMULA

Consists of the numbers 0, 1, 3, 5, 9, 11, 17, 29, 41, 2*4^m, 6*4^m and 14*4^m (m >= 0). Compare A123069.

From 224 on, a(n) = 4*a(n-3).

Numbers n such that A025428(n) = 0.

MATHEMATICA

q=22; lst={}; Do[Do[Do[Do[z=a^2+b^2+c^2+d^2; If[z<=q^2+3, AppendTo[lst, z]], {d, q}], {c, q}], {b, q}], {a, q}]; lst1=Union@lst lst={}; Do[AppendTo[lst, n], {n, q^2+3}]; lst2=lst Complement[lst2, lst1] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2010 *)

Join[{0, 1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41}, LinearRecurrence[{0, 0, 4}, {56, 96, 128}, 30]] (* Jean-François Alcover, Feb 09 2016 *)

PROG

(PARI) for(n=1, 224, if(sum(a=1, n, sum(b=1, a, sum(c=1, b, sum(d=1, c, if(a^2+b^2+c^2+d^2-n, 0, 1)))))==0, print1(n, ", ")))

(PARI) {a(n)=if(n<1, 0, if(n<15, [1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41][n], [4, 7, 12][(n+1)%3+1]*2^((n+1)\3*2-7)))} /* Michael Somos, Apr 08 2006 */

(PARI) {a(n)=if(n<2, 0, if(n<16, [1, 2, 3, 5, 6, 8, 9, 11, 14, 17, 24, 29, 32, 41][n-1], [4, 7, 12][n%3+1]*2^(n\3*2-7)))} /* Michael Somos, Apr 23 2006 */

(PARI) is(n)=my(k=if(n, n/4^valuation(n, 4), 2)); k==2 || k==6 || k==14 || setsearch([0, 1, 3, 5, 9, 11, 17, 29, 41], n) \\ Charles R Greathouse IV, Sep 03 2014

CROSSREFS

Cf. A123069, A000414 (complement).

Sequence in context: A139791 A027563 A219729 * A136112 A127936 A280771

Adjacent sequences:  A000531 A000532 A000533 * A000535 A000536 A000537

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane and J. H. Conway

STATUS

approved

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Last modified May 30 00:42 EDT 2017. Contains 287304 sequences.