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A103612
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Number of solutions to 5+B^2=p^2+q^2 with B=2n, p,q>0 and 2p^2<5+B^2.
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0
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1, 1, 0, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 1, 0, 0, 2, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 1, 0, 0, 0, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 1, 1, 0, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,16
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COMMENTS
| The number of matrices with entries in Z to G^2=G+1 not of the form gI or g'I (g, the golden number and g'=1-g are the solutions to x^2=x+1), hence of the form (1+p q-B | q+B 1-p) with p^2+q^2=5+B^2 is given by 8a(n) for n!=1 and by 4a(1)=4 for n=1.
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EXAMPLE
| a(0)=1 because 5+0^2=5=1^2+2^2. a(15)=2 because 5+30^2=905=8^2+29^2=11^2+28^2.
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CROSSREFS
| Cf. A104768.
Sequence in context: A093955 A081603 A165277 * A083913 A023670 A188170
Adjacent sequences: A103609 A103610 A103611 * A103613 A103614 A103615
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KEYWORD
| easy,nonn
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AUTHOR
| Michele Dondi (blazar(AT)lcm.mi.infn.it), Mar 24 2005
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