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A153285 a(1)=1; for n > 1, a(n) = n^2 + Sum_{j=1..n-1} (-1)^j*a(j).

%I A153285 #23 Sep 08 2022 08:45:39
%S A153285 1,3,11,7,23,11,35,15,47,19,59,23,71,27,83,31,95,35,107,39,119,43,131,
%T A153285 47,143,51,155,55,167,59,179,63,191,67,203,71,215,75,227,79,239,83,
%U A153285 251,87,263,91,275,95,287,99,299,103,311,107,323,111,335,115,347,119,359
%N A153285 a(1)=1; for n > 1, a(n) = n^2 + Sum_{j=1..n-1} (-1)^j*a(j).
%C A153285 1 followed by interleaving of A004767 and A017653. - _Klaus Brockhaus_, Jan 04 2009
%H A153285 Antti Karttunen, <a href="/A153285/b153285.txt">Table of n, a(n) for n = 1..10000</a>
%H A153285 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,2,0,-1).
%F A153285 a(n) = 2n-1 if n is 1 or an even number;
%F A153285 a(n) = 6n-7 if n is an odd number other than 1.
%F A153285 G.f.: x*(1 + 3*x + 9*x^2 + x^3 + 2*x^4)/((1+x)^2*(1-x)^2). - _Klaus Brockhaus_, Oct 15 2009
%F A153285 a(n) = 4*(n-1) - (2*n-3)*(-1)^n for n>1, a(1)=1. - _Bruno Berselli_, Sep 14 2011
%e A153285 a(1) = 1;
%e A153285 a(2) = 2^2 - a(1) = 4 - 1 = 3;
%e A153285 a(3) = 3^2 + a(2) - a(1) = 9 + 3 - 1 = 11;
%e A153285 a(4) = 4^2 - 11 + 3 - 1 = 7;
%e A153285 a(5) = 25 + 7 - 11 + 3 - 1 = 23;
%e A153285 a(6) = 36 - 23 + 7 - 11 + 3 - 1 = 11; etc.
%o A153285 (Magma) S:=[ 1 ]; for n in [2..61] do Append(~S, n^2 + &+[ (-1)^j*S[j]: j in [1..n-1] ]); end for; S; // _Klaus Brockhaus_, Jan 04 2009
%o A153285 (Scheme) (define (A153285 n) (cond ((= 1 n) n) ((even? n) (+ n n -1)) (else (+ (* 6 n) -7)))) ;; _Antti Karttunen_, Aug 10 2017
%Y A153285 The second of a family of sequences that includes A153284 and A153286
%Y A153285 Cf. A004767 (4n+3), A017653 (12n+11). - _Klaus Brockhaus_, Jan 04 2009
%K A153285 nonn,easy
%O A153285 1,2
%A A153285 _Walter Carlini_, Dec 23 2008
%E A153285 Extended beyond a(30) by _Klaus Brockhaus_, Jan 04 2009