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Search: id:A129111
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| A129111 |
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Sums of three consecutive heptagonal numbers. |
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+0
1
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| 8, 26, 59, 107, 170, 248, 341, 449, 572, 710, 863, 1031, 1214, 1412, 1625, 1853, 2096, 2354, 2627, 2915, 3218, 3536, 3869, 4217, 4580, 4958, 5351, 5759, 6182, 6620, 7073, 7541, 8024, 8522, 9035, 9563, 10106, 10664, 11237, 11825, 12428, 13046, 13679
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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Arises in heptagonal number analogue to A129803 Triangular numbers which are the sum of three consecutive triangular numbers. What are the heptagonal numbers which are the sum of three consecutive heptagonal numbers? Prime for a(2) = 59, a(3) = 107, a(7) = 449, a(10) = 863, a(11) = 1031, a(23) = 4217, a(26) = 5351, a(31) = 7541, a(42) = 13679, a(43) = 14327, a(46) = 16361, a(51) = 20051.
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FORMULA
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a(n) = Hep(n) + Hep(n+1) + Hep(n+2) where Hep(n) = A000566(n) = n(5n-3)/2. a(n) = (15/2)*n^2 + (21/2)*n + 8.
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EXAMPLE
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a(0) = Hep(0) + Hep(1) + Hep(2) = 0 + 1 + 7 = 8 = (15/2)*0^2 + (21/2)*0 + 8.
a(1) = Hep(1) + Hep(2) + Hep(3) = 1 + 7 + 18 = 26 = (15/2)*1^2 + (21/2)*1 + 8.
a(2) = Hep(2) + Hep(3) + Hep(4) = 7 + 18 + 34 = 59 = (15/2)*2^2 + (21/2)*2 + 8.
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CROSSREFS
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Cf. A000566, A007667, A034961, A129803, A129863.
Adjacent sequences: A129108 A129109 A129110 this_sequence A129112 A129113 A129114
Sequence in context: A085690 A005897 A111694 this_sequence A002413 A002901 A050471
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost2(AT)yahoo.com), May 24 2007
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