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

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A285113a(n0) = if1, a(n<1) = 2, for n+ > 1, a(n) = 2 +sum( Sum_{k=1,..(n-1),bitor(binomial} C(n-1,k-1), OR C(n-1,k), where C(n,k) is binomial(n coefficient and OR is bitwise-1,k)))OR (A003986);.

a(0) = 1, a(1) = 2, for n > 1, a(n) = 2 + Sum_{k=1..(n-1)} C(n-1,k-1) OR C(n-1,k), where C(n,k) is a binomial coefficient and OR is bitwise-OR (A003986).

Row sums of A285116: a(n) = 2 + Sum_{k=1..(n-1)} (C(n-1,k-1) bitwise-or C(n-1,k)), a(0) = 1, a(1) = 2.

a(0) = 1, a(1) = 2, for n > 1, a(n) = 2 + Sum_{k=1..(n-1)} C(n-1,k-1) OR C(n-1,k), where C(n,k) is a binomial coefficient and OR is a bitwise-OR (A003986).

A285113(n) = if(n<2,n+1,2+sum(k=1,(n-1),bitor(binomial(n-1,k-1),binomial(n-1,k))));

a(0) = 1, a(1) = 2, for n > 1, a(n) = 2 + Sum_{k=1..(n-1)} C(n-1,k-1) OR C(n-1,k), where C(n,k) is a binomial coefficient and OR is a bitwise-OR (A003986).

Cf. A000079, A003986, A007318, A285114, A285115, A285116.

Antti Karttunen, <a href="/A285113/b285113.txt">Table of n, a(n) for n = 0..256</a>

(PARI) A285113(n) = if(n<2, n+1, 2+sum(k=1, (n-1), bitor(binomial(n-1, k-1), binomial(n-1, k))));

allocated for Antti KarttunenRow sums of A285116.

1, 2, 3, 8, 11, 24, 52, 108, 207, 448, 720, 1376, 2892, 5544, 12532, 23448, 47239, 98112, 186672, 377896, 743656, 1519816, 2983160, 6354536, 11975324, 25917040, 48312920, 100406048, 196868844, 397726592, 788233496, 1578253728, 3225757559, 6275638528, 13012144160, 25792000088, 51825463000, 104303846272, 206598440472

0,2

a(n) = A285114(n) + A285115(n).

a(n) = A000079(n) - A285115(n).

(Scheme)

(define (A285113 n) (add A285116 (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)))))))

Cf. A000079, A285114, A285115, A285116.

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Antti Karttunen, Apr 16 2017

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allocated for Antti Karttunen

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