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A077768
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Number of times that the sum of two squares is an integer between n^2 and (n+1)^2; multiple representations are counted multiply.
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3
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1, 2, 2, 3, 4, 4, 6, 7, 7, 7, 8, 10, 10, 11, 11, 12, 13, 15, 15, 14, 18, 17, 17, 19, 19, 21, 20, 21, 23, 22, 26, 25, 26, 27, 25, 29, 27, 32, 30, 28, 33, 33, 36, 34, 33, 37, 36, 39, 38, 40, 39, 38, 42, 40, 46, 43, 45, 44, 46, 48, 47, 49, 50, 48, 50, 50, 53, 55, 52, 55, 53, 60, 57
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Related to the circle problem, cf. A077770. Note that 2*a(n)-A077770(n)/4 is the characteristic sequence for the Beatty sequence A001951. See A077769 for a more restrictive case. A077773 counts multiple representations only once.
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EXAMPLE
| a(8)=7 because 65=64+1, 65=49+16, 68=64+4, 72=36+36, 73=64+9, 74=49+25 and 80=64+16 are between squares 64 and 81. Note that 65 occurs twice.
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MATHEMATICA
| maxN=100; lst={}; For[n=1, n<=maxN, n++, cnt=0; i=n; j=0; While[i>=j, j=1; While[i^2+j^2<(n+1)^2, If[i>=j&&i^2+j^2>n^2, cnt++ ]; j++ ]; i--; j-- ]; AppendTo[lst, cnt]]; lst
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CROSSREFS
| Cf. A001951, A077769, A077770.
Sequence in context: A138374 A029936 A114093 * A143038 A029040 A053281
Adjacent sequences: A077765 A077766 A077767 * A077769 A077770 A077771
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KEYWORD
| nonn
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Nov 20 2002
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