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.

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

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