A007306 -id:A007306 - cp's OEIS frontend

A284268 Sum of coefficients > 1 in the Stern polynomial B(2n+1,x): a(n) = A275812(A277324(n)).

0, 0, 2, 0, 2, 3, 4, 0, 2, 6, 7, 5, 5, 6, 6, 0, 2, 8, 9, 9, 10, 11, 11, 7, 7, 11, 12, 9, 8, 9, 8, 0, 2, 10, 12, 11, 13, 17, 16, 12, 13, 18, 20, 16, 15, 17, 15, 9, 9, 15, 17, 16, 17, 19, 18, 12, 11, 16, 17, 13, 11, 12, 10, 0, 2, 12, 15, 14, 17, 22, 21, 15, 17, 25, 27, 24, 23, 26, 22, 15, 16, 24, 29, 26, 28, 32, 30, 21, 20, 28, 30, 24, 21, 23, 19, 11, 11, 19

Offset: 0

Antti Karttunen, Mar 25 2017

nonn

Sum of terms larger than one on row 2n+1 of table A125184.

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A007306, A125184, A260443, A275812, A277324, A284267.

Odd bisection of A284272.

A003961[p_?PrimeQ] := A003961[p] = Prime[ PrimePi[p] + 1]; A003961[1] = 1; A003961[n_] := A003961[n] = Times @@ (A003961[First[#]] ^ Last[#] & ) /@ FactorInteger[n] (* after Jean-François Alcover, Dec 01 2011 *); A260443[n_]:= If[n<2, n + 1, If[EvenQ[n], A003961[A260443[n/2]], A260443[(n - 1)/2] * A260443[(n + 1)/2]]]; A275812[n_]:= PrimeOmega[n] - If[n<2, 0,Count[Transpose[FactorInteger[n]][[2]], 1]]; Table[A275812[A260443[2n + 1]], {n, 0, 150}] (* Indranil Ghosh, Mar 28 2017 *)

A284268(n) = A284272(n+n+1); \\ Other code as in A284272.

(define (A284268 n) (A284272 (+ n n 1)))
(define (A284268 n) (A275812 (A277324 n)))

a(n) = A284272((2*n)+1).
a(n) = A275812(A277324(n)).
Other identities. For all n >= 0:
A007306(1+n) = A284267(n) + a(n).

A284565 Bisection of A000360.

Original entry on oeis.org

1, 1, 1, 2, 2, 2, 3, 2, 2, 4, 4, 3, 4, 4, 3, 3, 3, 4, 6, 5, 5, 7, 6, 4, 5, 6, 6, 6, 5, 5, 5, 3, 3, 6, 7, 6, 8, 9, 8, 7, 7, 9, 11, 9, 8, 10, 8, 5, 6, 8, 9, 9, 9, 10, 10, 7, 6, 9, 9, 7, 7, 7, 5, 4, 4, 6, 9, 8, 9, 12, 11, 8, 10, 13, 14, 13, 12, 13, 12, 8, 8, 13, 15, 13, 15, 17, 15, 12, 11, 14, 16, 13, 11, 13, 10, 6, 7, 10

Offset: 0

Antti Karttunen, Apr 05 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A000360, A001222, A007306, A284556, A284563, A284566.

a[n_] := a[n] = Which[n == 0, 1, EvenQ@ n, a[n/2] + a[n/2 - 1], True, a[(n - 1)/2] - Mod[(n - 1)/2 - 1, 3] + 1]; Table[a[2 n], {n, 0, 97}] (* Michael De Vlieger, Apr 05 2017, after Jean-François Alcover at A000360 *)

(define (A284565 n) (A001222 (A284563 n)))
(define (A284565 n) (A000360with_prep_0 (+ n n 1))) ;; See code in A284556.

a(n) = A000360(2n).
a(n) = A001222(A284563(n)).
Other identities. For all n >= 1:
A007306(n) = a(n-1) + A284566(n-1).

A284566 Odd bisection of A284556.

Original entry on oeis.org

0, 1, 2, 1, 2, 3, 2, 2, 3, 3, 4, 4, 3, 4, 4, 2, 3, 5, 5, 5, 6, 6, 6, 5, 4, 6, 7, 5, 5, 6, 4, 3, 4, 5, 7, 7, 7, 9, 9, 6, 7, 10, 10, 9, 9, 9, 8, 6, 5, 8, 10, 8, 9, 11, 9, 7, 7, 8, 9, 8, 6, 7, 6, 3, 4, 7, 8, 8, 10, 11, 11, 9, 9, 13, 15, 12, 12, 14, 11, 8, 9, 12, 15, 14, 14, 17, 16, 11, 11, 15, 15, 13, 12, 12, 10, 7, 6

Offset: 0

Antti Karttunen, Apr 05 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A001222, A007306, A284556, A284564, A284565.

a[n_] := Which[n < 2, n, EvenQ@ n, a[n/2], True, a[(n - 1)/2] + a[(n + 1)/2]]; Table[(a[#] - JacobiSymbol[#, 3])/2 &[2 n + 1], {n, 0, 96}] (* Michael De Vlieger, Apr 05 2017 *)

(define (A284566 n) (A284556 (+ n n 1)))
(define (A284566 n) (A001222 (A284564 n)))

a(n) = A284556((2*n)+1).
a(n) = A001222(A284564(n)).
Other identities. For all n >= 1:
A007306(n) = a(n-1) + A284565(n-1).

A285106 a(n) = A001222(A284576(n)).

Original entry on oeis.org

1, 2, 2, 3, 4, 5, 3, 4, 5, 7, 7, 6, 7, 8, 4, 5, 6, 8, 8, 9, 10, 10, 8, 8, 8, 10, 10, 9, 10, 11, 5, 6, 7, 9, 11, 10, 14, 16, 14, 13, 14, 13, 15, 17, 14, 16, 10, 10, 10, 11, 15, 14, 15, 17, 15, 13, 11, 13, 13, 12, 13, 14, 6, 7, 8, 10, 14, 13, 15, 19, 21, 17, 18, 20, 24, 25, 22, 20, 20, 16, 17, 19, 25, 23, 25, 30, 20, 22, 20, 20, 26, 26

Offset: 0

Antti Karttunen, Apr 11 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A001222, A003986, A007306, A284576, A285107, A285108.

(define (A285106 n) (A001222 (A284576 n)))
;; A more practical version, needing only an implementation of A003986bi (bitwise-or, A003986) and memoization-macro definec:
(define (A285106 n) (apply + (bitwise_or_of_exp_lists (A260443as_coeff_list n) (A260443as_coeff_list (+ 1 n)))))
(define (bitwise_or_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (bitwise_or_of_exp_lists nums2 nums1)) (else (map A003986bi nums1 (append nums2 (make-list (- len1 len2) 0)))))))
(definec (A260443as_coeff_list n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_coeff_list (/ n 2)))) (else (add_two_lists (A260443as_coeff_list (/ (- n 1) 2)) (A260443as_coeff_list (/ (+ n 1) 2))))))
(define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))

a(n) = A001222(A284576(n)).
a(n) = A285107(n) + A285108(n).
Other identities. For all n >= 0:
A007306(1+n) = a(n) + A285108(n).

A285107 a(n) = A001222(A284577(n)).

Original entry on oeis.org

1, 2, 1, 3, 4, 5, 1, 4, 5, 7, 6, 5, 7, 8, 1, 5, 6, 7, 5, 8, 9, 7, 4, 7, 7, 8, 7, 7, 10, 11, 1, 6, 7, 7, 8, 7, 13, 14, 11, 13, 14, 7, 9, 16, 11, 13, 4, 9, 9, 6, 11, 11, 12, 13, 11, 12, 9, 9, 8, 9, 13, 14, 1, 7, 8, 7, 11, 10, 11, 15, 20, 17, 17, 14, 19, 25, 20, 13, 17, 16, 17, 13, 20, 19, 21, 26, 9, 21, 18, 11, 21, 26, 17, 19, 4, 11, 11, 6, 17, 17, 18, 15, 9

Offset: 0

Antti Karttunen, Apr 11 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A001222, A003987, A007306, A284577, A285106, A285108.

(define (A285107 n) (A001222 (A284577 n)))
;; A more practical version, needing only an implementation of A003987bi (bitwise-xor, A003987) and memoization-macro definec:
(define (bitwise_xor_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (bitwise_xor_of_exp_lists nums2 nums1)) (else (map A003987bi nums1 (append nums2 (make-list (- len1 len2) 0)))))))
(definec (A260443as_coeff_list n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_coeff_list (/ n 2)))) (else (add_two_lists (A260443as_coeff_list (/ (- n 1) 2)) (A260443as_coeff_list (/ (+ n 1) 2))))))
(define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))

a(n) = A001222(A284577(n)).
a(n) = A285106(n) - A285108(n).
Other identities. For all n >= 0:
A007306(1+n) = a(n) + 2*A285108(n).

A285108 a(n) = A001222(A284578(n)).

Original entry on oeis.org

0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 1, 0, 0, 3, 0, 0, 1, 3, 1, 1, 3, 4, 1, 1, 2, 3, 2, 0, 0, 4, 0, 0, 2, 3, 3, 1, 2, 3, 0, 0, 6, 6, 1, 3, 3, 6, 1, 1, 5, 4, 3, 3, 4, 4, 1, 2, 4, 5, 3, 0, 0, 5, 0, 0, 3, 3, 3, 4, 4, 1, 0, 1, 6, 5, 0, 2, 7, 3, 0, 0, 6, 5, 4, 4, 4, 11, 1, 2, 9, 5, 0, 3, 3, 8, 1, 1, 7, 4, 3, 4, 8, 10, 3, 3, 11, 6, 3, 4, 9, 4, 1, 1, 5, 5, 3, 3, 5, 4, 1

Offset: 0

Antti Karttunen, Apr 11 2017

nonn

Antti Karttunen, Table of n, a(n) for n = 0..8192

Cf. A001222, A004198, A007306, A284578, A285106, A285107.

(define (A285108 n) (A001222 (A284578 n)))
;; A more practical version, needing only an implementation of A004198bi (bitwise-and, A004198) and memoization-macro definec:
(define (A285108 n) (apply + (bitwise_and_of_exp_lists (A260443as_coeff_list n) (A260443as_coeff_list (+ 1 n)))))
(define (bitwise_and_of_exp_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (bitwise_and_of_exp_lists nums2 nums1)) (else (map A004198bi nums1 (append nums2 (make-list (- len1 len2) 0)))))))
(definec (A260443as_coeff_list n) (cond ((zero? n) (list)) ((= 1 n) (list 1)) ((even? n) (cons 0 (A260443as_coeff_list (/ n 2)))) (else (add_two_lists (A260443as_coeff_list (/ (- n 1) 2)) (A260443as_coeff_list (/ (+ n 1) 2))))))
(define (add_two_lists nums1 nums2) (let ((len1 (length nums1)) (len2 (length nums2))) (cond ((< len1 len2) (add_two_lists nums2 nums1)) (else (map + nums1 (append nums2 (make-list (- len1 len2) 0)))))))

a(n) = A001222(A284578(n)).
a(n) = A285106(n) - A285107(n).
Other identities. For all n >= 0:
A007306(1+n) = A285106(n) + a(n) = A285107(n) + 2*a(n).

A054427 Permutation of natural numbers: maps the fractions A038567/A038566 to the right side (n/m > 1) of Stern-Brocot tree.

Original entry on oeis.org

1, 2, 4, 3, 8, 5, 16, 7, 6, 9, 32, 17, 64, 15, 13, 12, 10, 33, 128, 14, 11, 65, 256, 31, 25, 24, 18, 129, 512, 29, 20, 257, 1024, 63, 30, 28, 49, 48, 21, 19, 34, 513, 2048, 26, 23, 1025, 4096, 127, 61, 57, 27, 97, 96, 22, 40, 36, 66, 2049, 8192, 62, 56, 41, 35, 4097

Offset: 1

Antti Karttunen

nonn

			Right side of Stern-Brocot tree: 1/1 2/1 3/2 3/1 4/3 5/3 5/2 4/1 5/4 7/5 8/5 7/4 7/3 8/3 7/2 5/1
A038567/A038566: 1/1 2/1 3/1 3/2 4/1 4/3 5/1 5/2 5/3 5/4 6/1 6/5 7/1 7/2 7/3 7/4

A038567/A038566 = shift_left(A007306)/A047679(A054427(.)).

Inverse permutation: A054428.

A038567_A038566_to_SternBrocot_permutation := proc(u) local a,n,i; a := []; for n from 1 to u do for i from 1 to n do if (1 = igcd(n,i)) then a := [op(a),cfrac2binexp(convert((n/i),confrac))+1]; fi; od; od; RETURN(a); end; # cfrac2binexp given in A054424.

A273493 a(n) = A245327(n) + A245328(n).

Original entry on oeis.org

2, 3, 3, 5, 5, 4, 4, 8, 8, 7, 7, 7, 7, 5, 5, 13, 13, 11, 11, 12, 12, 9, 9, 11, 11, 10, 10, 9, 9, 6, 6, 21, 21, 18, 18, 19, 19, 14, 14, 19, 19, 17, 17, 16, 16, 11, 11, 18, 18, 15, 15, 17, 17, 13, 13, 14, 14, 13, 13, 11, 11, 7, 7, 34, 34, 29, 29, 31, 31, 23, 23, 30, 30, 27, 27, 25, 25, 17, 17, 31, 31, 26, 26, 29, 29, 22, 22, 25

Offset: 1

Yosu Yurramendi, May 23 2016

nonn

The terms (n>0) may be written as a left-justified array with rows of length 2^m, m >= 0:
2,
3, 3,
5, 5, 4, 4,
8, 8, 7, 7, 7, 7, 5, 5,
13,13,11,11,12,12, 9, 9,11,11,10,10, 9, 9, 6, 6,
21,21,18,18,19,19,14,14,19,19,17,17,16,16,11,11,18,18,15,15,17,17,13,13,14,14,...
All columns have the Fibonacci sequence property: a(2^(m+2) + k) = a(2^(m+1) + k) + a(2^m + k), m >= 0,  0 <= k < 2^m (empirical observations).
The terms (n>0) may also be written as a right-justified array with rows of length 2^m, m >= 0:
                                                                              2,
                                                                           3, 3,
                                                                     5, 5, 4, 4,
                                                         8, 8, 7, 7, 7, 7, 5, 5,
                                13,13,11,11,12,12, 9, 9,11,11,10,10, 9, 9, 6, 6,
    ...,19,19,17,17,16,16,11,11,18,18,15,15,17,17,13,13,14,14,13,13,11,11, 7, 7,
Each column is an arithmetic sequence. The differences of the arithmetic sequences repeat the sequence A071585: a(2^(m+2) -1 - 2k) - a(2^(m+1) -1 - 2k) = A071585(k-1),    m > 0,  0 <= k < 2^m ; a(2^(m+2) -1 - 2k - 1) - a(2^(m+1) -1 - 2k - 1) = A071585(k-1), m > 0,  0 <= k < 2^m .
n>1 occurs in this sequence phi(n) = A000010(n) times, as it occurs in A007306 (Franklin T. Adams-Watters' comment), that is the sequence obtained by adding numerator and denominator in the Calkin-Wilf enumeration system of positive rationals. A245327(n)/A245328(n) is also an enumeration system of all positive rationals, and in each level m >= 0 (ranks between 2^m and 2^(m+1)-1) rationals are the same in both systems. Thus a(n) has the same terms in each level as A007306.
a(n) = A273494(A059893(n)), a(A059893(n)) = A273494(n), n > 0. - Yosu Yurramendi, May 30 2017

Yosu Yurramendi, Table of n, a(n) for n = 1..4099

Cf. A007306, A268087, A071585, A086592, A273494

b(n) = my(b=binary(n)); fromdigits(concat(b[1], Vecrev(vector(#b-1, k, b[k+1]))), 2); \\ from A059893
a(n) = my(n=b(n), x=1, y=1); for(i=0, logint(n, 2), if(bittest(n, i), [x, y]=[x+y, y], [x, y]=[y, x+y])); x \\ Mikhail Kurkov, Mar 11 2023

a(n) = A007306(A284459(n)), n > 0. - Yosu Yurramendi, Aug 23 2021

A273494 a(n) = A245325(n) + A245326(n).

Original entry on oeis.org

2, 3, 3, 5, 4, 5, 4, 8, 7, 7, 5, 8, 7, 7, 5, 13, 11, 12, 9, 11, 10, 9, 6, 13, 11, 12, 9, 11, 10, 9, 6, 21, 18, 19, 14, 19, 17, 16, 11, 18, 15, 17, 13, 14, 13, 11, 7, 21, 18, 19, 14, 19, 17, 16, 11, 18, 15, 17, 13, 14, 13, 11, 7, 34, 29, 31, 23, 30, 27, 25, 17, 31, 26, 29, 22, 25, 23, 20, 13, 29, 25, 26, 19, 27, 24, 23, 16, 23

Offset: 1

Yosu Yurramendi, May 23 2016

nonn

The terms (n>0) may be written as a left-justified array with rows of length 2^m, m >= 0:
   2,
   3, 3,
   5, 4, 5, 4,
   8, 7, 7, 5, 8, 7, 7, 5,
  13,11,12, 9,11,10, 9, 6,13,11,12, 9,11,10, 9, 6,
  21,18,19,14,19,17,16,11,18,15,17,13,14,13,11, 7,21,18,19,14,19,17,...
All columns have the Fibonacci sequence property: a(2^(m+2) + k) = a(2^(m+1) + k) + a(2^m + k), m >= 0, 0 <= k < 2^m (empirical observations).
The terms (n>0) may also be written as a right-justified array with rows of length 2^m, m >= 0:
                                                                           2,
                                                                        3, 3,
                                                                  5, 4, 5, 4,
                                                      8, 7, 7, 5, 8, 7, 7, 5,
                             13,11,12, 9,11,10, 9, 6,13,11,12, 9,11,10, 9, 6,
..., 18,15,17,13,14,13,11, 7,21,18,19,14,19,17,16,11,18,15,17,13,14,13,11, 7,
Each column is an arithmetic sequence. The differences of the arithmetic sequences give the sequence A071585: a(2^(m+1)-1-k) - a(2^m-1-k) = A071585(k), m >= 0, 0 <= k < 2^m.
n > 1 occurs in this sequence phi(n) = A000010(n) times, as it occurs in A007306 (Franklin T. Adams-Watters's comment), which is the sequence obtained by adding numerator and denominator in the Calkin-Wilf enumeration system of positive rationals. A245325(n)/A245326(n) is also an enumeration system of all positive rationals, and in each level m >= 0 (ranks between 2^m and 2^(m+1)-1) rationals are the same in both systems. Thus a(n) has the same terms in each level as A007306.
The same property occurs in all numerator+denominator sequences of enumeration systems of positive rationals, as, for example, A007306 (A007305+A047679), A071585 (A229742+A071766), A086592 (A020650+A020651), A268087 (A162909+A162910).

Yosu Yurramendi, Table of n, a(n) for n = 1..4095

Cf. A007306, A268087, A071585, A086592, A273493

a(n) = my(x=1, y=1); for(i=0, logint(n, 2), if(bittest(n, i), [x, y]=[x+y, y], [x, y]=[y, x+y])); x \\ Mikhail Kurkov, Mar 10 2023

a(n) = A273493(A059893(n)), a(A059893(n)) = A273493(n), n > 0. - Yosu Yurramendi, May 30 2017

a(n) = A007306(A059893(A180200(n))) = A007306(A059894(A154435(n))). - Yosu Yurramendi, Sep 20 2021

A282714 Base-2 generalized Pascal triangle P_2 read by rows (see Comments for precise definition).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 2, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 2, 1, 0, 0, 1, 1, 3, 0, 3, 0, 0, 0, 1, 1, 1, 3, 0, 3, 0, 0, 0, 1, 1, 2, 2, 1, 1, 2, 0, 0, 0, 1, 1, 2, 3, 1, 1, 1, 1, 0, 0, 0, 1, 1, 3, 1, 3, 0, 2, 0, 1, 0, 0, 0, 1, 1, 2, 4, 1, 2, 0, 2, 0, 0

Offset: 0

N. J. A. Sloane, Mar 02 2017

List the binary numbers in their natural order as binary strings, beginning with the empty string epsilon, which represents 0. Row n of the triangle gives the number of times the k-th string occurs as a (scattered) substring of the n-th string.

Row n has sum n+1.

			Triangle begins:
  1,
  1,1,
  1,1,1,
  1,2,0,1,
  1,1,2,0,1,
  1,2,1,1,0,1,
  1,2,2,1,0,0,1,
  1,3,0,3,0,0,0,1,
  1,1,3,0,3,0,0,0,1
  1,2,2,1,1,2,0,0,0,1
  1,2,3,1,1,1,1,0,0,0,1
  1,3,1,3,0,2,0,1,0,0,0,1
  1,2,4,1,2,0,2,0,0,0,0,0,1
  ...
The binary numbers are epsilon, 1, 10, 11, 100, 101, 110, 111, 1000, ...
The fifth number 101 contains
eps 1 10 11 100 101 respectively
.1..2..1..1...0...1 times, which is row 5 of the triangle.

Lars Blomberg, Table of n, a(n) for n = 0..10000
Julien Leroy, Michel Rigo, Manon Stipulanti, Counting the number of non-zero coefficients in rows of generalized Pascal triangles, Discrete Mathematics 340 (2017), 862-881.
Julien Leroy, Michel Rigo, Manon Stipulanti, Counting Subwords Occurrences in Base-b Expansions, arXiv:1705.10065 [math.CO], 2017.
Julien Leroy, Michel Rigo, Manon Stipulanti, Counting Subwords Occurrences in Base-b Expansions, Integers, Electronic Journal of Combinatorial Number Theory 18A (2018), #A13.
Manon Stipulanti, Convergence of Pascal-Like Triangles in Parry-Bertrand Numeration Systems, arXiv:1801.03287 [math.CO], 2018.

A007306 gives (essentially) the number of nonzero entries in the rows.

Nscatsub := proc(subw,w)
    local lsubw,lw,N,wri,wr,i ;
    lsubw := nops(subw) ;
    lw := nops(w) ;
    N := 0 ;
    if lsubw = 0 then
        return 1 ;
    elif lsubw > lw then
        return 0 ;
    else
        for wri in combinat[choose](lw,lsubw) do
            wr := [] ;
            for i in wri do
                wr := [op(wr),op(i,w)] ;
            end do:
            if verify(subw,wr,'sublist') then
                N := N+1 ;
            end if;
        end do:
    end if;
    return N ;
end proc:
P := proc(n,k,b)
    local n3,k3 ;
    n3 := convert(n,base,b) ;
    k3 := convert(k,base,b) ;
    Nscatsub(k3,n3) ;
end proc:
A282714 := proc(n,k)
    P(n,k,2) ;
end proc: # R. J. Mathar, Mar 03 2017

nmax = 12;
row[n_] := Module[{bb, ss}, bb = Table[IntegerDigits[k, 2], {k, 0, n}]; ss = Subsets[Last[bb]]; Prepend[Count[ss, #]& /@ bb // Rest, 1]];
Table[row[n], {n, 0, nmax}] // Flatten (* Jean-François Alcover, Dec 14 2017 *)

More terms from Lars Blomberg, Mar 03 2017

cp's OEIS Frontend

A284268 Sum of coefficients > 1 in the Stern polynomial B(2n+1,x): a(n) = A275812(A277324(n)).

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Scheme

Formula

A284565 Bisection of A000360.

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Mathematica

Scheme

Formula

A284566 Odd bisection of A284556.

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Mathematica

Scheme

Formula

A285106 a(n) = A001222(A284576(n)).

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Scheme

Formula

A285107 a(n) = A001222(A284577(n)).

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A285108 a(n) = A001222(A284578(n)).

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Scheme

Formula

A054427 Permutation of natural numbers: maps the fractions A038567/A038566 to the right side (n/m > 1) of Stern-Brocot tree.

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Maple

A273493 a(n) = A245327(n) + A245328(n).

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PARI

Formula

A273494 a(n) = A245325(n) + A245326(n).