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A006597
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a(n) = n^2*(5*n-3)/2.
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6
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0, 1, 14, 54, 136, 275, 486, 784, 1184, 1701, 2350, 3146, 4104, 5239, 6566, 8100, 9856, 11849, 14094, 16606, 19400, 22491, 25894, 29624, 33696, 38125, 42926, 48114, 53704, 59711, 66150, 73036, 80384, 88209, 96526, 105350, 114696, 124579, 135014, 146016
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OFFSET
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0,3
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COMMENTS
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Structured heptagonal prism numbers. - James A. Record (james.record(AT)gmail.com), Nov 07 2004
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REFERENCES
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W. A. Whitworth, DCC Exercises in Choice and Chance, Stechert, NY, 1945, p. 29.
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LINKS
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FORMULA
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a(n) = (1/6)*(15*n^3-9*n^2). - James A. Record (james.record(AT)gmail.com), Nov 07 2004
a(n) = Sum_{i=0..n-1} n*(5*i+1) for n>0. [Bruno Berselli, Sep 08 2015]
Sum_{n>=1} 1/a(n) = 1.1080093773051638036... = (sqrt(5*(5 - 2*sqrt(5)))*Pi - Pi^2 - 5*sqrt(5)*arccoth(sqrt(5)) + (25*log(5))/2)/9. - Vaclav Kotesovec, Oct 04 2016
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MAPLE
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MATHEMATICA
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PROG
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CROSSREFS
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Cf. A100177 - structured prisms; A100145 for more on structured numbers.
Cf. similar sequences, with the formula (k*n-k+2)*n^2/2, listed in A262000.
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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