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%I #58 Mar 02 2023 13:45:12
%S 10,20,74,100,202,244,394,452,650,724,970,1060,1354,1460,1802,1924,
%T 2314,2452,2890,3044,3530,3700,4234,4420,5002,5204,5834,6052,6730,
%U 6964,7690,7940,8714,8980,9802,10084,10954,11252,12170,12484,13450,13780,14794,15140
%N 1^2 + 3^2, 2^2 + 4^2, 5^2 + 7^2, 6^2 + 8^2, ...
%H Colin Barker, <a href="/A276764/b276764.txt">Table of n, a(n) for n = 1..1000</a>
%H Quora, <a href="https://www.quora.com/What-is-the-next-number-in-this-sequence-10-20-74-100">What is the next number in this sequence: 10, 20, 74, 100?</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F a(n) = (2n - 1 - ((n+1) mod 2))^2 + (2n + (n mod 2))^2.
%F From _Colin Barker_, Nov 10 2016: (Start)
%F G.f.: 2*x*(5 + 5*x + 17*x^2 + 3*x^3 + 2*x^4) / ((1 - x)^3 * (1 + x)^2).
%F a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5) for n>5.
%F a(n) = 8*n^2 - 8*n + 4 for n even.
%F a(n) = 8*n^2 + 2 for n odd.
%F (End)
%t LinearRecurrence[{1,2,-2,-1,1},{10,20,74,100,202},50] (* _Harvey P. Dale_, Mar 02 2023 *)
%o (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
%Y Cf. A001844.
%K nonn,easy
%O 1,1
%A _Edwin McCravy_, Nov 06 2016
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