A386660 a(n) = Sum_{k=1..n} binomial(n, k) (mod 2^k).
1, 1, 5, 7, 11, 29, 37, 67, 115, 225, 353, 635, 719, 2321, 3417, 3959, 7071, 9301, 22973, 35231, 62315, 71029, 246613, 338987, 544675, 855673, 1775777, 2960467, 3427695, 7422841, 16357769, 21442879, 27029999, 64048845, 75934141, 235944023, 323818203, 611090685, 512203269, 1789628291
Offset: 1
Keywords
Examples
The sum a(n) = Sum_{k=1..n} binomial(n, k) (mod 2^k) is illustrated below.
a(1) = 1 = 1;
a(2) = 0 + 1 = 1;
a(3) = 1 + 3 + 1 = 5;
a(4) = 0 + 2 + 4 + 1 = 7;
a(5) = 1 + 2 + 2 + 5 + 1 = 11;
a(6) = 0 + 3 + 4 + 15 + 6 + 1 = 29;
a(7) = 1 + 1 + 3 + 3 + 21 + 7 + 1 = 37;
a(8) = 0 + 0 + 0 + 6 + 24 + 28 + 8 + 1 = 67;
a(9) = 1 + 0 + 4 + 14 + 30 + 20 + 36 + 9 + 1 = 115;
a(10) = 0 + 1 + 0 + 2 + 28 + 18 + 120 + 45 + 10 + 1 = 225;
a(11) = 1 + 3 + 5 + 10 + 14 + 14 + 74 + 165 + 55 + 11 + 1 = 353;
a(12) = 0 + 2 + 4 + 15 + 24 + 28 + 24 + 239 + 220 + 66 + 12 + 1 = 635;
a(13) = 1 + 2 + 6 + 11 + 7 + 52 + 52 + 7 + 203 + 286 + 78 + 13 + 1 = 719;
a(14) = 0 + 3 + 4 + 9 + 18 + 59 + 104 + 187 + 466 + 1001 + 364 + 91 + 14 + 1 = 2321;
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Links
- Chai Wah Wu, Table of n, a(n) for n = 1..4299 (terms 1..1000 from Paul D. Hanna)
Programs
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PARI
{a(n) = sum(k=1,n,binomial(n, k) % 2^k)} for(n=1,40,print1(a(n),", "))
Comments