

A165601


Midpoint height of Jacobibridge, computed for 4n+3. a(n) = Sum_{i=0..(2n+1)} J(i,4n+3), where J(i,m) is the Jacobi symbol.


13



1, 1, 3, 2, 3, 3, 1, 3, 6, 4, 3, 5, 6, 4, 9, 2, 3, 7, 2, 5, 9, 6, 6, 8, 0, 5, 9, 8, 6, 10, 6, 5, 15, 2, 9, 10, 0, 7, 12, 10, 3, 11, 6, 2, 15, 8, 6, 13, 12, 9, 12, 0, 9, 14, 12, 7, 15, 12, 6, 15, 1, 6, 21, 12, 12, 13, 6, 11, 0, 6, 9, 14, 12, 8, 24, 10, 9, 19, 0, 10, 12, 12, 9, 18, 18, 1, 15
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OFFSET

0,3


LINKS

A. Karttunen, Table of n, a(n) for n = 0..269535


MATHEMATICA

Table[Sum[JacobiSymbol[i, 4n + 3], {i, 0, 2n + 1}], {n, 0, 100}] (* Indranil Ghosh, May 13 2017 *)


PROG

(MIT Scheme:)
(define (A165601 n) (let ((w (A004767 n))) (add (lambda (i) (jacobisymbol i w)) 0 (/ (1+ w) 2))))
(define (add intfun lowlim uplim) (let sumloop ((i lowlim) (res 0)) (cond ((> i uplim) res) (else (sumloop (1+ i) (+ res (intfun i)))))))
(define jacobisymbol fix:jacobisymbol)
(define (fix:jacobisymbol p q) (if (not (and (fix:fixnum? p) (fix:fixnum? q) (fix:= 1 (fix:and q 1)))) (error "fix:jacobisymbol: args must be fixnums, and 2. arg should be odd: " p q) (let loop ((p p) (q q) (s 0)) (cond ((fix:zero? p) 0) ((fix:= 1 p) (fix: 1 (fix:and s 2))) ((fix:= 1 (fix:and p 1)) (loop (fix:remainder q p) p (fix:xor s (fix:and p q)))) (else (loop (fix:lsh p 1) q (fix:xor s (fix:xor q (fix:lsh q 1)))))))))
(PARI) a(n) = sum(i=0, 2*n + 1, kronecker(i, 4*n + 3)); \\ Indranil Ghosh, May 13 2017
(Python)
from sympy import jacobi_symbol as J
def a(n): return sum([J(i, 4*n + 3) for i in xrange(2*n + 2)]) # Indranil Ghosh, May 13 2017


CROSSREFS

Trisections: A165604, A165605, A165606.
Cf. A165602, A165603, A165460, A166045, A166046, A166047.
Sequence in context: A230406 A214254 A153092 * A275821 A291674 A265157
Adjacent sequences: A165598 A165599 A165600 * A165602 A165603 A165604


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 06 2009


STATUS

approved



