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A243579 Integers of the form 8k+7 that can be written as a sum of four distinct squares of the form m, m+2, m+4, m+5, where m == 1 (mod 4). 6
71, 255, 567, 1007, 1575, 2271, 3095, 4047, 5127, 6335, 7671, 9135, 10727, 12447, 14295, 16271, 18375, 20607, 22967, 25455, 28071, 30815, 33687, 36687, 39815, 43071, 46455, 49967, 53607, 57375, 61271, 65295, 69447, 73727, 78135, 82671, 87335, 92127, 97047, 102095, 107271, 112575, 118007, 123567, 129255, 135071, 141015, 147087 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If n is of the form 8k+7 and n = a^2+b^2+c^2+d^2 with gap pattern 221, then [a,b,c,d] = [1,3,5,6]+[4*i,4*i,4*i,4*i] for i>=0.

LINKS

Walter Kehowski, Table of n, a(n) for n = 1..20737

J. Owen Sizemore, Lagrange's Four Square Theorem

R. C. Vaughan, Lagrange's Four Square Theorem

Eric Weisstein's World of Mathematics, Lagrange's Four-Square Theorem

Wikipedia, Lagrange's four-square theorem

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = 64*n^2-8*n+15.

From Colin Barker, Sep 13 2015: (Start)

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) for n>3.

G.f.: -x*(15*x^2+42*x+71) / (x-1)^3.

(End)

EXAMPLE

a(5) = 64*5^2-8*5+15 = 1575 and m = 4*5-3 = 17 so 1575 = 17^2+19^2+21^2+22^2.

MAPLE

A243579 := proc(n::posint) return 64*n^2-8*n+15 end;

PROG

(PARI) Vec(-x*(15*x^2+42*x+71)/(x-1)^3 + O(x^100)) \\ Colin Barker, Sep 13 2015

CROSSREFS

Cf. A008586, A016813, A016825, A004767, A243577, A243578, A243579, A243580, A243581, A243582

Sequence in context: A325079 A142325 A232475 * A142013 A033240 A298103

Adjacent sequences:  A243576 A243577 A243578 * A243580 A243581 A243582

KEYWORD

nonn,easy

AUTHOR

Walter Kehowski, Jun 08 2014

STATUS

approved

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Last modified April 3 00:35 EDT 2020. Contains 333195 sequences. (Running on oeis4.)