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A276764
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1^2 + 3^2, 2^2 + 4^2, 5^2 + 7^2, 6^2 + 8^2, ...
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1
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10, 20, 74, 100, 202, 244, 394, 452, 650, 724, 970, 1060, 1354, 1460, 1802, 1924, 2314, 2452, 2890, 3044, 3530, 3700, 4234, 4420, 5002, 5204, 5834, 6052, 6730, 6964, 7690, 7940, 8714, 8980, 9802, 10084, 10954, 11252, 12170, 12484, 13450, 13780, 14794, 15140
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) = (2n - 1 - ((n+1) mod 2))^2 + (2n + (n mod 2))^2.
G.f.: 2*x*(5 + 5*x + 17*x^2 + 3*x^3 + 2*x^4) / ((1 - x)^3 * (1 + x)^2).
a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5.
a(n) = 8*n^2 - 8*n + 4 for n even.
a(n) = 8*n^2 + 2 for n odd.
(End)
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MATHEMATICA
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LinearRecurrence[{1, 2, -2, -1, 1}, {10, 20, 74, 100, 202}, 50] (* Harvey P. Dale, Mar 02 2023 *)
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PROG
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(PARI) Vec(2*x*(5+5*x+17*x^2+3*x^3+2*x^4) / ((1-x)^3*(1+x)^2) + O(x^60)) \\ Colin Barker, Nov 10 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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