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A122769
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Numbers k such that k^2 is of the form 3*m^2 + 2*m + 1 (A056109).
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1
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1, 11, 153, 2131, 29681, 413403, 5757961, 80198051, 1117014753, 15558008491, 216695104121, 3018173449203, 42037733184721, 585510091136891, 8155103542731753, 113585939507107651, 1582048049556775361
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OFFSET
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1,2
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COMMENTS
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All terms are odd. Sequence is infinite. Corresponding m's are 0, 6, 88, 1230, 17136, 238678, 3324360, 46302366, 644908768, 8982420390, 125108976696, 1742543253358, 24270496570320. s^2 are squares in A056109.
The Diophantine equation A000290(x) = A000326(y) + A000326(y-1) has the solutions x = a(n) and y = (4^n + (1 + sqrt(3))^(4*n - 3) + (1 - sqrt(3))^(4*n - 3))/(3*2^(2*n - 1)). - Bruno Berselli, Mar 04 2013
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LINKS
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FORMULA
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Alternatively, with a different offset:
a(0) = 1, a(1) = 11, a(n) = 14*a(n-1) - a(n-2), and
a(n) = ((3 - b)*(7 - 4*b)^n + (3 + b)*(7 + 4*b)^n)/6, b = sqrt(3).
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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