A092413 Coefficient of x^n in solution of x = y + y^2 + y^4 + y^8 + ...

1, -1, 2, -6, 20, -70, 256, -970, 3772, -14960, 60280, -246090, 1015700, -4231216, 17767456, -75126078, 319588340, -1366846548, 5873832384, -25350152100, 109828012448, -477486940848, 2082520454864, -9109146150050, 39950535931956

Offset

1,3

Comments

Reversion of Fredholm-Rueppel sequence (A036987) shifted right.

Links

Table of n, a(n) for n=1..25.

Formula

From Paul D. Hanna, Nov 14 2025: (Start)

G.f. A(x) satisfies the following formulas.

(1) x = Sum_{n>=0} A(x)^(2^n) by definition.

(2) x = A( Sum_{n>=0} x^(2^n) ).

(3) x^(2^n) = A( Sum_{k>=n} x^(2^k) ) for n >= 1.

(4) A(x)^2 = A(x - A(x)).

(5) A(x)^4 = A(x - A(x) - A(x)^2).

(6) A(x)^8 = A(x - A(x) - A(x)^2 - A(x)^4).

(7) A(x)^(2^n) = A( x - Sum_{k=0..n-1} A(x)^(2^k) ) for n >= 1.

(8) A(x)^(2^n) = A( Sum_{k>=n} A(x)^(2^k) ) for n >= 1. (End)

Maple

# Using function CompInv from A357588.
CompInv(25, n -> if 2^ilog2(n) = n then 1 else 0 fi); # Peter Luschny, Oct 05 2022

Prog

(PARI) serreverse(sum(k=0, 8, x^(2^k))+O(x^257))

Crossrefs

Cf. A036987, A049140.

Sequence in context: A340891 A049140 A372526 * A151285 A150126 A150127

Adjacent sequences: A092410 A092411 A092412 * A092414 A092415 A092416

Keyword

sign

Author

Ralf Stephan, Mar 22 2004

Status

approved