0,2

This sequence equals the left-most column of a rectangular table formed

by starting with the positive integers in row 0, then generating row n+1

by removing terms in positions {(k+1)*(k+2)/2 - 2, k>=1} out of row n:

[ (1), 2, 3, (4), 5, 6, 7, (8), 9,10,11,12,(13),14,15,16,17,18,(19),...];

[ (2), 3, 5, (6), 7, 9,10,(11),12,14,15,16,(17),18,20,21,22,23,(24),...];

[ (3), 5, 7, (9),10,12,14,(15),16,18,20,21,(22),23,25,27,28,29,(30),...];

[ (5), 7,10,(12),14,16,18,(20),21,23,25,27,(28),29,31,33,35,36,(37),...];

[ (7),10,14,(16),18,21,23,(25),27,29,31,33,(35),36,38,40,42,44,(45),...];

[(10),14,18,(21),23,27,29,(31),33,36,38,40,(42),44,46,48,50,52,(54),...];

[(14),18,23,(27),29,33,36,(38),40,44,46,48,(50),52,55,57,59,61,(63),...];

[(18),23,29,(33),36,40,44,(46),48,52,55,57,(59),61,65,67,69,71,(73),...]; ...

For each row, removing terms enclosed in parenthesis forms the next row.

(PARI) {a(n)=polcoeff((1-x+x^2)/(1-x)^3 - x*sum(k=0, 10, x^(k+2^k))/(1-x +x*O(x^n))^2, n)}

Sequence in context: A115024 A167050 A019529 this_sequence A025488 A088585 A008581

Adjacent sequences: A130050 A130051 A130052 this_sequence A130054 A130055 A130056

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), May 03 2007