Search: id:a072474
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A072474
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Sum of next n squares.
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+0
13
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1, 13, 77, 294, 855, 2071, 4403, 8492, 15189, 25585, 41041, 63218, 94107, 136059, 191815, 264536, 357833, 475797, 623029, 804670, 1026431, 1294623, 1616187, 1998724, 2450525, 2980601, 3598713, 4315402, 5142019, 6090755, 7174671
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = k(k+1)(2k+1)/6 - r(r+1)(2r+1)/6, where k = n(n+1)/2 and r = n(n-1)/2.
G.f.: x*(1+3*x+x^2)*(1+4*x+x^2)/(1-x)^6. - Colin Barker, Mar 23 2012
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 6. - Jinyuan Wang, May 25 2020
E.g.f.: exp(x)*x*(12 + 66*x + 82*x^2 + 30*x^3 + 3*x^4)/12. - Stefano Spezia, May 14 2024
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EXAMPLE
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1^2 = 1; 2^2 + 3^2 = 13; 4^2 + 5^2 + 6^2 = 77; ...
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MATHEMATICA
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Table[Sum[ i^2, {i, n(n - 1)/2 + 1, n(n + 1)/2}], {n, 1, 35}]
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PROG
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(PARI) for(n=1, 50, print1(n*(3*n^2+1)*(n^2+2)/12, ", "))
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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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EXTENSIONS
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STATUS
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approved
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