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A256646
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26-gonal pyramidal numbers: a(n) = n*(n+1)*(8*n-7)/2.
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2
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0, 1, 27, 102, 250, 495, 861, 1372, 2052, 2925, 4015, 5346, 6942, 8827, 11025, 13560, 16456, 19737, 23427, 27550, 32130, 37191, 42757, 48852, 55500, 62725, 70551, 79002, 88102, 97875, 108345, 119536, 131472, 144177, 157675, 171990, 187146, 203167, 220077
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (24th row of the table).
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LINKS
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FORMULA
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G.f.: x*(1 + 23*x)/(1 - x)^4.
Sum_{n>=1} 1/a(n) = 2*(4*(sqrt(2)+1)*Pi - 4*(sqrt(2)-8)*log(2) + 8*sqrt(2)*log(sqrt(2)+2) - 7)/105. - Amiram Eldar, Jan 10 2022
E.g.f.: (1/2)*x*(2 + 25*x + 8*x^2)*exp(x). - G. C. Greubel, Jul 12 2024
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MATHEMATICA
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Table[n (n + 1) (8 n - 7)/2, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 27, 102}, 40] (* Vincenzo Librandi, Apr 08 2015 *)
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PROG
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(SageMath) [(8*n-7)*binomial(n+1, 2) for n in range(51)] # G. C. Greubel, Jul 12 2024
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CROSSREFS
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Cf. similar sequences listed in A237616.
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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