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A269735 G.f.: Sum_{k >= 0} x^(2^k)*(1-x^(2^k))/(1+x^(2^k)). 3
0, 1, -1, 2, -3, 2, 0, 2, -5, 2, 0, 2, -2, 2, 0, 2, -7, 2, 0, 2, -2, 2, 0, 2, -4, 2, 0, 2, -2, 2, 0, 2, -9, 2, 0, 2, -2, 2, 0, 2, -4, 2, 0, 2, -2, 2, 0, 2, -6, 2, 0, 2, -2, 2, 0, 2, -4, 2, 0, 2, -2, 2, 0, 2, -11, 2, 0, 2, -2, 2, 0, 2, -4, 2, 0, 2, -2, 2, 0, 2, -6, 2, 0, 2, -2, 2, 0, 2, -4, 2, 0, 2, -2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Second differences of A268289.

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..65537

MAPLE

t7:=add(x^(2^k)*(1-x^(2^k))/(1+x^(2^k)), k=0..12);

t8:=series(t7, x, 256);

PROG

(PARI)

up_to = 1024;

A268289list(up_to) =  { my(v=vector(up_to), s = 1); v[1] = s; for(n=2, up_to, s += (2*hammingweight(n) - #binary(n)); v[n] = s); (v); };

v268289 = A268289list(up_to+1);

A268289(n) = if(!n, n, v268289[n]);

almost_firstdiffs_of_A268289(n) = if(!n, 1, v268289[n+1]-v268289[n]);

A269735(n) = if(n<=1, n, almost_firstdiffs_of_A268289(n-1)-almost_firstdiffs_of_A268289(n-2)); \\ Antti Karttunen, Sep 30 2018

(PARI)

up_to_k = 16;

up_to = 1+(2^up_to_k);

x='x+O('x^(up_to+1));

v269735 = Vec(sum(k=0, up_to_k, x^(2^k)*(1-x^(2^k))/(1+x^(2^k))));

A269735(n) = if(!n, n, v269735[n]); \\ Antti Karttunen, Oct 01 2018

CROSSREFS

Cf. A268289, A187038.

Sequence in context: A226556 A007325 A247920 * A187038 A332260 A056619

Adjacent sequences:  A269732 A269733 A269734 * A269736 A269737 A269738

KEYWORD

sign

AUTHOR

N. J. A. Sloane, Mar 11 2016

STATUS

approved

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Last modified March 7 19:49 EST 2021. Contains 341931 sequences. (Running on oeis4.)