A079492 Nearest integer to Sum_{k=0..n} binomial(n,k)/2^(k*(k-1)/2).

1, 2, 4, 6, 9, 12, 17, 23, 31, 41, 52, 66, 82, 101, 124, 150, 180, 215, 254, 299, 351, 408, 473, 546, 628, 719, 820, 932, 1055, 1192, 1342, 1508, 1689, 1887, 2104, 2340, 2597, 2876, 3179, 3507, 3863, 4247, 4662, 5108, 5590, 6107, 6663, 7259, 7899, 8583, 9316, 10099

Offset

0,2

References

D. L. Kreher and D. R. Stinson, Combinatorial Algorithms, CRC Press, 1999, p. 113.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Example

1, 2, 7/2, 45/8, 545/64, 12625/1024, 564929/32768, 49162689/2097152, ...

Maple

f := n->add(binomial(n, k)/2^(k*(k-1)/2), k=0..n);

Mathematica

Table[Round[Sum[Binomial[n, k]/2^(k*(k-1)/2), {k, 0, n}]], {n, 0, 60}] (* G. C. Greubel, Jan 18 2019 *)

Prog

(PARI) vector(60, n, n--; round(sum(k=0, n, binomial(n, k)/2^(k*(k-1)/2)))) \\ G. C. Greubel, Jan 18 2019
(Magma) [Round( (&+[Binomial(n, k)/2^(k*(k-1)/2): k in [0..n]]) ): n in [0..60]]; // G. C. Greubel, Jan 18 2019
(Sage) [round(sum(binomial(n, k)/2^(k*(k-1)/2) for k in (0..30))) for n in (0..60)] # G. C. Greubel, Jan 18 2019

Crossrefs

Cf. A079491.

Sequence in context: A102379 A238374 A133041 * A267161 A173784 A094660

Adjacent sequences: A079489 A079490 A079491 * A079493 A079494 A079495

Keyword

nonn

Author

N. J. A. Sloane, Jan 20 2003

Status

approved