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Search: id:A129863
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| A129863 |
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Sums of three consecutive pentagonal numbers. |
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+0
5
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| 6, 18, 39, 69, 108, 156, 213, 279, 354, 438, 531, 633, 744, 864, 993, 1131, 1278, 1434, 1599, 1773, 1956, 2148, 2349, 2559, 2778, 3006, 3243, 3489, 3744, 4008, 4281, 4563, 4854, 5154, 5463, 5781, 6108, 6444, 6789, 7143, 7506, 7878, 8259, 8649, 9048, 9456
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Arises in pentagonal number analogue to A129803 Triangular numbers which are the sum of three consecutive triangular numbers. What are the pentagonal numbers which are the sum of three consecutive pentagonal numbers?
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FORMULA
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a(n) = P(n) + P(n+1) + P(n+2) where P(n) = A000326(n) = n(3n-1)/2.
a(n) = P(n) + P(n+1) + P(n+2) where P(n) = A000326(n) = n(3n-1)/2. For n = 0, 1, 2, ... a(n+1) = (9/2)*(n^2) + (15/2)*n + 6.
a(n) = (3n^2+5n+4)*(3/2) - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 27 2007
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EXAMPLE
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a(1) = 6 = A000326(0) + A000326(1) + A000326(2) = 0 + 1 + 5.
a(2) = 18 = A000326(1) + A000326(2) + A000326(3) = 1 + 5 + 12.
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MATHEMATICA
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Table[(3/2)*(4 + 5*n + 3*n^2), {n, 0, 100}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), May 27 2007
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CROSSREFS
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Cf. A000326, A007667, A034961, A129803.
Sequence in context: A101853 A132432 A005899 this_sequence A035489 A122061 A002411
Adjacent sequences: A129860 A129861 A129862 this_sequence A129864 A129865 A129866
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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 23 2007, May 24 2007
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