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Search: id:A129109
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| A129109 |
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Sums of three consecutive hexagonal numbers. |
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1
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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
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OFFSET
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0,1
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COMMENT
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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
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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
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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
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Cf. A000384, A007667, A034961, A129803, A129863.
Sequence in context: A132438 A010001 A014073 this_sequence A002412 A041215 A060822
Adjacent sequences: A129106 A129107 A129108 this_sequence A129110 A129111 A129112
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), May 24 2007
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