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A256645
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25-gonal pyramidal numbers: a(n) = n*(n+1)*(23*n-20)/6.
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9
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0, 1, 26, 98, 240, 475, 826, 1316, 1968, 2805, 3850, 5126, 6656, 8463, 10570, 13000, 15776, 18921, 22458, 26410, 30800, 35651, 40986, 46828, 53200, 60125, 67626, 75726, 84448, 93815, 103850, 114576, 126016, 138193, 151130, 164850, 179376, 194731, 210938
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OFFSET
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0,3
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COMMENTS
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If b(n,k) = n*(n+1)*((k-2)*n-(k-5))/6 is n-th k-gonal pyramidal number, then b(n,k) = A000292(n) + (k-3)*A000292(n-1) (see Deza in References section, p. 96).
Also, b(n,k) = b(n,k-1) + A000292(n-1) (see Deza in References section, p. 95). Some examples:
This is the case k=25.
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REFERENCES
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E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 93 (23rd row of the table).
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LINKS
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FORMULA
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G.f.: x*(1 + 22*x)/(1 - x)^4.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>3. - Colin Barker, Apr 07 2015
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MATHEMATICA
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Table[n (n + 1) (23 n - 20)/6, {n, 0, 40}]
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 26, 98}, 40] (* Vincenzo Librandi, Apr 08 2015 *)
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PROG
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(PARI) concat(0, Vec(x*(1 + 22*x)/(1 - x)^4 + O(x^100))) \\ Colin Barker, Apr 07 2015
(Magma) k:=25; [n*(n+1)*((k-2)*n-(k-5))/6: n in [0..40]]; // Vincenzo Librandi, Apr 08 2015
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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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