A274642 Numbers of the form 4^k*(8*j+7) that have exactly three partitions into four positive squares.

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

Colin Barker, Table of n, a(n) for n = 1..1000

D. H. Lehmer, Draft of Math Review of paper by Om Prakash Srivastava, Sep 18 1957.

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]

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

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

Adjacent sequences: A274639 A274640 A274641 * A274643 A274644 A274645

Keyword

nonn,easy

Author

N. J. A. Sloane, Jul 09 2016

Status

approved