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A274642
Numbers of the form 4^k*(8*j+7) that have exactly three partitions into four positive squares.
1
28, 55, 60, 79, 92, 95, 112, 240, 368, 448, 960, 1472, 1792, 3840, 5888, 7168, 15360, 23552, 28672, 61440, 94208, 114688, 245760, 376832, 458752, 983040, 1507328, 1835008, 3932160, 6029312, 7340032, 15728640, 24117248, 29360128, 62914560, 96468992, 117440512, 251658240, 385875968, 469762048, 1006632960
OFFSET
1,1
LINKS
Om Prakash Srivastava, On the number of representations as sum of four squares of numbers of the form 4^a(8b+7), Journal of Scientific Research, Banaras Hindu University, VI(2) (1955-1956), 278-285. [Annotated scanned copy]
FORMULA
Consists of 55, 79, 95, and the numbers 4^k*m where k >= 1 and m is 7, 15, or 23.
From Colin Barker, Jul 10 2016: (Start)
a(n) = 4*a(n-3) for n>9.
G.f.: x*(28+55*x+60*x^2-33*x^3-128*x^4-145*x^5-204*x^6-128*x^7-12*x^8) / (1-4*x^3).
(End)
EXAMPLE
55 is a member because we have 55 = 49+4+1+1 = 36+9+9+1 = 25+25+4+1.
MATHEMATICA
LinearRecurrence[{0, 0, 4}, {28, 55, 60, 79, 92, 95, 112, 240, 368}, 50] (* Harvey P. Dale, May 06 2019 *)
PROG
(PARI) Vec(x*(28+55*x+60*x^2-33*x^3-128*x^4-145*x^5-204*x^6-128*x^7-12*x^8) / (1-4*x^3) + O(x^50)) \\ Colin Barker, Jul 10 2016
CROSSREFS
Sequence in context: A044461 A056028 A120372 * A068129 A079731 A119168
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jul 09 2016
STATUS
approved