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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. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A322757 A010666 A196001 * A182757 A164515 A298871
KEYWORD
nonn,easy
AUTHOR
Brian Hopkins, Apr 28 2015
STATUS
approved

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Last modified March 18 22:56 EDT 2024. Contains 370952 sequences. (Running on oeis4.)