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A072277
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Smallest integer > 1 which is both n-gonal and centered n-gonal.
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0
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10, 25, 51, 91, 148, 225, 325, 451, 606, 793, 1015, 1275, 1576, 1921, 2313, 2755, 3250, 3801, 4411, 5083, 5820, 6625, 7501, 8451, 9478, 10585, 11775, 13051, 14416, 15873, 17425, 19075, 20826, 22681, 24643, 26715, 28900, 31201, 33621, 36163
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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FORMULA
| a(n) = (n^3-n^2+2)/2.
a(3)=10, a(4)=25, a(5)=51, a(6)=91, a(n)=4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) [From Harvey P. Dale, Aug 19 2011]
G.f.: x^3*(-3*x^3+11*x^2-15*x+10)/(x-1)^4 [From Harvey P. Dale, Aug 19 2011]
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EXAMPLE
| a(4) = 25 is both square and centered square.
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MATHEMATICA
| LinearRecurrence[{4, -6, 4, -1}, {10, 25, 51, 91}, 50] (* or *) Table[(n^3-n^2+ 2)/2, {n, 3, 50}] (* From Harvey P. Dale, Aug 19 2011 *)
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CROSSREFS
| Sequence in context: A024838 A020179 A022670 * A063424 A137930 A071289
Adjacent sequences: A072274 A072275 A072276 * A072278 A072279 A072280
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KEYWORD
| nonn,easy
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net), Jul 09 2002
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