A153286 a(n) = n^3 + sum((-1)^j*a(j)); for j=1 to n-1; a(1)=1.

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

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