A285115 Row sums of A285118: a(n) = Sum_{k=1..(n-1)} (C(n-1,k-1) bitwise-and C(n-1,k)), a(0) = a(1) = 0.

0, 0, 1, 0, 5, 8, 12, 20, 49, 64, 304, 672, 1204, 2648, 3852, 9320, 18297, 32960, 75472, 146392, 304920, 577336, 1211144, 2034072, 4801892, 7637392, 18795944, 33811680, 71566612, 139144320, 285508328, 569229920, 1069209737, 2314296064, 4167725024, 8567738280, 16894013736, 33135107200, 68279466472, 121133055024

Offset: 0

Author

Antti Karttunen, Apr 16 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..256

Crossrefs

Cf. A000079, A004198, A007318, A285113, A285114, A285118.

Programs

Mathematica

a[n_]:=If[n<2, 0, Sum[BitAnd[Binomial[n - 1,k - 1], Binomial[n - 1, k]], {k, n - 1}]]; Table[a[n], {n, 0, 100}] (* Indranil Ghosh, Apr 16 2017 *)

PARI

A285115(n) = if(n<2,0,sum(k=1,(n-1),bitand(binomial(n-1,k-1),binomial(n-1,k))));

Scheme

(define (A285115 n) (add A285118 (A000217 n) (+ -1 (A000217 (+ 1 n)))))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (+ 1 i) (+ res (intfun i)))))))

Formula

a(0) = a(1) = 0, and for n > 1, a(n) = Sum_{k=1..(n-1)} C(n-1,k-1) AND C(n-1,k), where C(n,k) is a binomial coefficient & AND is bitwise-AND (A004198).

a(n) = A285113(n) - A285114(n).

a(n) = A000079(n) - A285113(n) = (A000079(n) - A285114(n))/2.