A257542 Square-sum pairs: Numbers n such that 0,1, ..., 2n-1 can be partitioned into n pairs, where each pair adds up to a perfect square.

1, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75

Offset

1,2

Comments

Kilkelly uses induction to prove that all integers greater than 20 are in the sequence after using various methods on smaller cases.

The positive integers except 2, 3, and 6.

The positive integers except the strong divisors of 6. - Omar E. Pol, Apr 30 2015

References

T. Kilkelly, The ARML Power Contest, American Mathematical Society, 2015, chapter 11.

Links

Table of n, a(n) for n=1..72.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

From Chai Wah Wu, Aug 13 2020: (Start)

a(n) = 2*a(n-1) - a(n-2) for n > 5.

G.f.: x*(-x^4 + x^3 - 2*x^2 + 2*x + 1)/(x - 1)^2. (End)

Example

For n = 4: (0, 1), (2, 7), (3, 6), (4, 5)
For n = 7: (0, 9), (1, 8), (2, 7), (3, 13), (4, 12), (5, 11), (6, 10)

Prog

(PARI) is(n)=n>6 || n==1 || n==4 || n==5 \\ Charles R Greathouse IV, Apr 30 2015

Crossrefs

Cf. A253472, A252897.

Sequence in context: A322757 A010666 A196001 * A182757 A164515 A298871

Adjacent sequences: A257539 A257540 A257541 * A257543 A257544 A257545

Keyword

nonn,easy

Author

Brian Hopkins, Apr 28 2015

Status

approved