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A261995 The first of four consecutive positive integers the sum of the squares of which is equal to the sum of the squares of twenty-one consecutive positive integers. 2
42, 123, 315, 1827, 4659, 13650, 34794, 201114, 512610, 1501539, 3827187, 22120875, 56382603, 165155802, 420955938, 2433095298, 6201573882, 18165636843, 46301326155, 267618362067, 682116744579, 1998054897090, 5092724921274, 29435586732234, 75026640329970 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

For the first of the corresponding twenty-one consecutive positive integers, see A261996.

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (1,0,0,110,-110,0,0,-1,1).

FORMULA

G.f.: -3*x*(6*x^8+8*x^6+27*x^5-596*x^4+504*x^3+64*x^2+27*x+14) / ((x-1)*(x^8-110*x^4+1)).

EXAMPLE

42 is in the sequence because 42^2 + ... + 45^2 = 7574 = 8^2 + ... + 28^2.

PROG

(PARI) Vec(-3*x*(6*x^8+8*x^6+27*x^5-596*x^4+504*x^3+64*x^2+27*x+14)/((x-1)*(x^8-110*x^4+1)) + O(x^40))

CROSSREFS

Cf. A157092, A246642, A261996.

Sequence in context: A113518 A044293 A044674 * A298236 A299362 A304613

Adjacent sequences:  A261992 A261993 A261994 * A261996 A261997 A261998

KEYWORD

nonn,easy

AUTHOR

Colin Barker, Sep 08 2015

STATUS

approved

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Last modified December 6 22:42 EST 2021. Contains 349567 sequences. (Running on oeis4.)