A130053 G.f. A(x) = (1-x+x^2)/(1-x)^3 - x*[Sum_{n>=0} x^(n + 2^n)]/(1-x)^2 .

1, 2, 3, 5, 7, 10, 14, 18, 23, 29, 36, 44, 52, 61, 71, 82, 94, 107, 121, 136, 152, 168, 185, 203, 222, 242, 263, 285, 308, 332, 357, 383, 410, 438, 467, 497, 528, 560, 592, 625, 659, 694, 730, 767, 805, 844, 884, 925, 967, 1010, 1054, 1099, 1145, 1192, 1240, 1289

Offset

0,2

Links

Table of n, a(n) for n=0..55.

Example

This sequence equals the leftmost 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 parentheses forms the next row.

Prog

(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)}

Crossrefs

Sequence in context: A019529 A194242 A173538 * A177277 A025488 A306473

Adjacent sequences: A130050 A130051 A130052 * A130054 A130055 A130056

Keyword

nonn

Author

Paul D. Hanna, May 03 2007

Status

approved