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A215147
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For n odd, a(n) = 1^2+2^2+3^2+...+n^2; for n even, a(n) = (1^2+2^2+3^2+...+n^2)+1.
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1
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1, 2, 5, 6, 14, 15, 30, 31, 55, 56, 91, 92, 140, 141, 204, 205, 285, 286, 385, 386, 506, 507, 650, 651, 819, 820, 1015, 1016, 1240, 1241, 1496, 1497, 1785, 1786, 2109, 2110, 2470, 2471, 2870, 2871, 3311, 3312, 3795, 3796, 4324, 4325, 4900, 4901, 5525, 5526
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OFFSET
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1,2
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COMMENTS
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Square pyramidal numbers when n is odd.
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LINKS
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FORMULA
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a(n) = (6*(5+3*(-1)^n)+(13-9*(-1)^n)*n-3*(-3+(-1)^n)*n^2+2*n^3)/48.
G.f.: -x*(x^6-x^5-2*x^4+2*x^3-x-1)/((x-1)^4*(x+1)^3). (End)
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MAPLE
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for i from 1 to 100 do a(2*i-1):=sum('k^2', 'k'=1..i);
a(2*i):=a(2*i-1)+1; end do;
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MATHEMATICA
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LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 2, 5, 6, 14, 15, 30}, 50] (* or *)
Riffle[#, #+1] & [Accumulate[Range[25]^2]] (* Paolo Xausa, Feb 22 2024 *)
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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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