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A363288 a(n) = (2*n^3 - n^2 + 3*n - 2)/2.

%I A363288 #26 Jun 05 2023 02:46:35
%S A363288 1,8,26,61,119,206,328,491,701,964,1286,1673,2131,2666,3284,3991,4793,
%T A363288 5696,6706,7829,9071,10438,11936,13571,15349,17276,19358,21601,24011,
%U A363288 26594,29356,32303,35441,38776,42314,46061,50023,54206,58616,63259,68141,73268,78646,84281
%N A363288 a(n) = (2*n^3 - n^2 + 3*n - 2)/2.
%C A363288 For n >= 3, a(n) is the sum of all multiples of n XOR n-1 that are <= n^2.
%H A363288 Winston de Greef, <a href="/A363288/b363288.txt">Table of n, a(n) for n = 1..10000</a>
%H A363288 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A363288 a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F A363288 a(n) = A002411(n) + (n-1)*A000217(n+1) - A046092(n-1).
%F A363288 a(n) = A162264(n-1) + 1 for n >= 2. - _Hugo Pfoertner_, Jun 02 2023
%F A363288 G.f.: x*(1 - 5*x + 2*x^2 - 4*x^3)/(1 - x)^4. - _Stefano Spezia_, Jun 03 2023
%t A363288 Table[(2 n^3 - n^2 + 3 n - 2)/2, {n, 100}]
%t A363288 LinearRecurrence[{4, -6, 4, -1}, {1, 8, 26, 61}, 50]
%o A363288 (Magma) [(2*n^3 - n^2 + 3*n - 2)/2 : n in [1..50]];
%o A363288 (PARI) a(n) = n^3 - 1 + (-n^2 + 3*n)/2 \\ _Winston de Greef_, Jun 01 2023
%Y A363288 Cf. A000217, A002411, A002414, A046092, A162264.
%K A363288 nonn,easy
%O A363288 1,2
%A A363288 _Wesley Ivan Hurt_, May 25 2023