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A129109
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Sums of three consecutive hexagonal numbers.
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0
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7, 22, 49, 88, 139, 202, 277, 364, 463, 574, 697, 832, 979, 1138, 1309, 1492, 1687, 1894, 2113, 2344, 2587, 2842, 3109, 3388, 3679, 3982, 4297, 4624, 4963, 5314, 5677, 6052, 6439, 6838, 7249, 7672, 8107, 8554, 9013, 9484, 9967, 10462, 10969, 11488
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Arises in hexagonal number analogue to A129803 Triangular numbers which are the sum of three consecutive triangular numbers. What are the hexagonal numbers which are the sum of three consecutive hexagonal numbers? Prime for a(0) = 7, a(4) = 139, a(6) = 277, a(8) = 463, a(18) = 2113, a(22) = 3109, a(26) = 4297, a(38) = 9013, a(40) = 9967.
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FORMULA
| a(n) = H(n) + H(n+1) + H(n+2) where H(n) = A000384(n) = n(2n-1). a(n) = 6*n^2 + 9*n + 7.
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EXAMPLE
| a(0) = H(0) + H(1) + H(2) = 0 + 1 + 6 = 7 = 6*0^2 + 9*0 + 7.
a(1) = H(1) + H(2) + H(3) = 1 + 6 + 15 = 22 = 6*1^2 + 9*1 + 7.
a(2) = H(2) + H(3) + H(4) = 6 + 15 + 28 = 49 = 6*2^2 + 9*2 + 7.
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CROSSREFS
| Cf. A000384, A007667, A034961, A129803, A129863.
Sequence in context: A010001 A197059 A014073 * A002412 A184629 A041215
Adjacent sequences: A129106 A129107 A129108 * A129110 A129111 A129112
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KEYWORD
| easy,nonn
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AUTHOR
| Jonathan Vos Post (jvospost3(AT)gmail.com), May 24 2007
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