A153286 - OEIS

%I #8 Sep 08 2022 08:45:39

%S 1,7,33,37,135,91,309,169,555,271,873,397,1263,547,1725,721,2259,919,

%T 2865,1141,3543,1387,4293,1657,5115,1951,6009,2269,6975,2611,8013,

%U 2977,9123,3367,10305,3781,11559,4219,12885,4681,14283,5167,15753,5677,17295

%N a(n) = n^3 + sum((-1)^j*a(j)); for j=1 to n-1; a(1)=1.

%C 1 followed by interleaving of A154105 and 3*A154106. - _Klaus Brockhaus_, Jan 04 2009

%F G.f.: x*(1 + 7*x + 30*x^2 + 16*x^3 + 39*x^4 + x^5 + 2*x^6)/((1+x)^3*(1-x)^3). - _Klaus Brockhaus_, Jan 04 2009

%F From _Walter Carlini_, Jan 12 2009: (Start)

%F a(n) = 3n^2 - 3n + 1 if n is 1 or an even number;

%F a(n) = 9n^2 - 21n + 15 if n is any odd number other than 1. (End)

%e a(1)=1, a(2)=2^3-a(1)=8-1=7, a(3)=3^3+a(2)-a(1)=27+7-1=33, a(4)=64-33+7-1=37, a(5)=125+37-33+7-1=135, a(6)=216-135+37-33+7-1=91, etc.

%o (Magma) S:=[ 1 ]; for n in [2..45] do Append(~S, n^3 + &+[ (-1)^j*S[j]: j in [1..n-1] ]); end for; S; // _Klaus Brockhaus_, Jan 04 2009

%Y The third of a family of sequences that includes A153284 and A153285.

%Y Cf. A154105 (12*n^2 + 18*n + 7), A154106 (12*n^2 + 22*n + 11). - _Klaus Brockhaus_, Jan 04 2009

%K easy,nonn

%O 1,2

%A _Walter Carlini_, Dec 23 2008, Jan 01 2009

%E Extended beyond a(30) by _Klaus Brockhaus_, Jan 04 2009

%E G.f. corrected by _Klaus Brockhaus_, Oct 15 2009