OFFSET
1,7
LINKS
Paul D. Hanna, Table of n, a(n) for n = 1..1030
FORMULA
a(2*n) = a(n) for n>=1.
EXAMPLE
G.f.: A(x) = x + x^2 + 1/2*x^3 + x^4 + 1/8*x^5 + 1/2*x^6 + 7/16*x^7 + x^8 - 21/128*x^9 + 1/8*x^10 + 71/256*x^11 + 1/2*x^12 + 5/1024*x^13 + 7/16*x^14 + 1095/2048*x^15 + x^16 - 15885/32768*x^17 - 21/128*x^18 + 18443/65536*x^19 + 1/8*x^20 - 55841/262144*x^21 + 71/256*x^22 + 324945/524288*x^23 + 1/2*x^24 - 2649857/4194304*x^25 + 5/1024*x^26 + 6109987/8388608*x^27 + 7/16*x^28 - 18206579/33554432*x^29 + 1095/2048*x^30 + 92290439/67108864*x^31 + x^32 +...+ a(n)*x^n/2^A274716(n) +...
such that ( A(x) - A(x^2) )^2 = A(x^2).
RELATED SERIES.
The following series forms an odd function:
A(x) - A(x^2) = x + 1/2*x^3 + 1/8*x^5 + 7/16*x^7 - 21/128*x^9 + 71/256*x^11 + 5/1024*x^13 + 1095/2048*x^15 - 15885/32768*x^17 + 18443/65536*x^19 - 55841/262144*x^21 + 324945/524288*x^23 - 2649857/4194304*x^25 + 6109987/8388608*x^27 - 18206579/33554432*x^29 +...
where ( A(x) - A(x^2) )^2 = A(x^2):
(A(x) - A(x^2))^2 = x^2 + x^4 + 1/2*x^6 + x^8 + 1/8*x^10 + 1/2*x^12 + 7/16*x^14 + x^16 - 21/128*x^18 + 1/8*x^20 + 71/256*x^22 + 1/2*x^24 + 5/1024*x^26 + 7/16*x^28 + 1095/2048*x^30 + x^32 +...
PROG
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Jul 07 2016
STATUS
approved