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A270867
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a(n) = n^3 + 2*n^2 + 4*n + 1.
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8
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1, 8, 25, 58, 113, 196, 313, 470, 673, 928, 1241, 1618, 2065, 2588, 3193, 3886, 4673, 5560, 6553, 7658, 8881, 10228, 11705, 13318, 15073, 16976, 19033, 21250, 23633, 26188, 28921, 31838, 34945, 38248, 41753, 45466, 49393, 53540, 57913, 62518, 67361, 72448
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OFFSET
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0,2
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COMMENTS
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Numbers of the type (m+1)^3 - (m-1)*m. Similar sequences are: A069778 with the closed form (m+1)^3 - m*(m+1), A152015 with (m+1)^3 - (m+1)*(m+2).
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LINKS
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FORMULA
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O.g.f.: (1 + 4*x - x^2 + 2*x^3)/(1 - x)^4.
E.g.f.: (1 + 7*x + 5*x^2 + x^3)*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
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MAPLE
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MATHEMATICA
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Table[n^3 + 2 n^2 + 4 n + 1, {n, 0, 40}]
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PROG
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(Magma) [n^3+2*n^2+4*n+1: n in [0..50]];
(PARI) x='x+O('x^99); Vec((1+4*x-x^2+2*x^3)/(1-x)^4) \\ Altug Alkan, Apr 01 2016
(Python) for i in range(0, 100):print(i**3+2*i**2+4*i+1) # Soumil Mandal, Apr 02 2016
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CROSSREFS
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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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