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 A153286 a(n) = n^3 + sum((-1)^j*a(j)); for j=1 to n-1; a(1)=1. 4
 1, 7, 33, 37, 135, 91, 309, 169, 555, 271, 873, 397, 1263, 547, 1725, 721, 2259, 919, 2865, 1141, 3543, 1387, 4293, 1657, 5115, 1951, 6009, 2269, 6975, 2611, 8013, 2977, 9123, 3367, 10305, 3781, 11559, 4219, 12885, 4681, 14283, 5167, 15753, 5677, 17295 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 1 followed by interleaving of A154105 and 3*A154106. - Klaus Brockhaus, Jan 04 2009 LINKS Table of n, a(n) for n=1..45. FORMULA 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 From Walter Carlini, Jan 12 2009: (Start) a(n) = 3n^2 - 3n + 1 if n is 1 or an even number; a(n) = 9n^2 - 21n + 15 if n is any odd number other than 1. (End) EXAMPLE 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. PROG (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 CROSSREFS The third of a family of sequences that includes A153284 and A153285. Cf. A154105 (12*n^2 + 18*n + 7), A154106 (12*n^2 + 22*n + 11). - Klaus Brockhaus, Jan 04 2009 Sequence in context: A324412 A373442 A175189 * A060745 A275163 A051895 Adjacent sequences: A153283 A153284 A153285 * A153287 A153288 A153289 KEYWORD easy,nonn AUTHOR Walter Carlini, Dec 23 2008, Jan 01 2009 EXTENSIONS Extended beyond a(30) by Klaus Brockhaus, Jan 04 2009 G.f. corrected by Klaus Brockhaus, Oct 15 2009 STATUS approved

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Last modified September 8 08:26 EDT 2024. Contains 375753 sequences. (Running on oeis4.)