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A050533
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Thickened pyramidal numbers: a(n) = 2*(n+1)*n + Sum_{i=1..n} (4*i*(i-1) + 1).
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3
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0, 5, 22, 59, 124, 225, 370, 567, 824, 1149, 1550, 2035, 2612, 3289, 4074, 4975, 6000, 7157, 8454, 9899, 11500, 13265, 15202, 17319, 19624, 22125, 24830, 27747, 30884, 34249, 37850, 41695, 45792, 50149, 54774, 59675, 64860, 70337, 76114, 82199
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = (1/3)*n*(5 + 6*n + 4*n^2) = binomial(2*n+1, 3) + 2*(n+1)*n = A000447(n) + 4*A000217(n).
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MATHEMATICA
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CoefficientList[Series[x*(5+2*x+x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 27 2012 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 5, 22, 59}, 40] (* Harvey P. Dale, May 08 2012 *)
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PROG
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(Magma) I:=[0, 5, 22, 59]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Apr 27 2012
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CROSSREFS
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KEYWORD
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nonn,easy,nice
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AUTHOR
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Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 29 1999
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STATUS
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approved
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