A157793 Convolution of numbers of binary zeros and ones.

0, 1, 1, 3, 2, 6, 6, 11, 8, 15, 15, 25, 21, 29, 29, 41, 33, 44, 43, 61, 53, 66, 67, 89, 76, 88, 85, 107, 96, 112, 112, 139, 119, 135, 130, 161, 144, 165, 166, 205, 180, 197, 191, 227, 209, 235, 237, 283, 250, 267, 256, 295, 269, 295, 293, 343, 308, 329, 319, 365, 339

Offset

0,4

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Formula

a(n) = Sum_{i=0..n} A023416(i)*A000120(n-i).

Mathematica

a[n_] := Sum[DigitCount[i, 2, 0]*DigitCount[n - i, 2, 1], {i, 0, n}]; Array[a, 100, 0] (* Amiram Eldar, Jul 16 2023 *)

Prog

(Haskell)
a157793 n = a157793_list !! n
a157793_list = f [head a023416_list] $ tail a023416_list where
   f zs (x:xs) = (sum $ zipWith (*) zs a000120_list) : f (x:zs) xs
-- Reinhard Zumkeller, Mar 31 2015

Crossrefs

Cf. A000120, A023416.

Sequence in context: A347743 A023360 A154028 * A096375 A062200 A114208

Adjacent sequences: A157790 A157791 A157792 * A157794 A157795 A157796

Keyword

nonn,base

Author

Reinhard Zumkeller, Mar 06 2009

Status

approved