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

Author

Walter Carlini, Dec 23 2008, Jan 01 2009

Keywords

• easy
• nonn

Comments

1 followed by interleaving of A154105 and 3*A154106. - Klaus Brockhaus, Jan 04 2009

Examples

			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.
		

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

Programs

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

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)

Extensions

Extended beyond a(30) by Klaus Brockhaus, Jan 04 2009

G.f. corrected by Klaus Brockhaus, Oct 15 2009