Syracuse Arms Co. was one of the few U.S. makers to use a "Washington" pattern; also called Ferlacher Austria 1, Bresilien, and Wellington by
Manufacture LiegeoiseClaude Gaier's
Four Centuries of Liege Gunmaking discusses the connection between US and Belgian firms. Ernest Heuse-Lemoine (1834-1926) from Nessonvaux was a major barrel maker in the Vesdre Valley maintaining agents in London, Birmingham, and New York. Every 3 years he would travel abroad and upon his return, would be met by a band in celebration because he always came back with more orders than his own firm could handle. He would then distribute some of the work to smaller barrel makers. Gaier states that Heuse-Lemoine supplied damascus barrels for at least 50 years to US makers, and that he invented the names of “Boston” and “Washington” damascus especially for the American market.
This is a refinished SAC "Washington". Remington called the pattern "Washington N 3. B.P." and unfortunately I don't believe anyone knows the significance of "N 3. B.P"

Note there are tiny rectangles within the scrolls; NOT crosses as with "American Flag", used a lot by Ithaca. Bro. Walt's Crass 4E

The "Star" or "American Flag" lopin is bottom left; the "Washington" is the 3rd on bottom

SAC barrels:
The hammer gun (first offered in 1904) was cataloged with “Triplett Steel” only, but several examples have been recorded with “New Twist” barrel tubes.
Grade 00 "Triplet Steel" (first offered in 1901);
Grade 0 and Grade 1 "New Twist";
Grade 2 and 3 "Improved Damascus"; (a few examples have been located with Krupp Steel barrels);
Grades A and A-1 Special Trap "Fine Damascus" or optional Krupp Steel;
Grade B and Grade C "Finest Grade Damascus" or optional Krupp Steel.
In the 1902 catalog, a new B Grade engraving style was introduced and the Damascus barrel was upgraded from "Fine Quality Damascus" to "Finest Grade Damascus".
Grade C guns were furnished with the "Finest Grade of Damascus Steel of very fine figure, fully warranted".
The D Grade gun, which retailed in 1901 for $475, was shipped with "the finest Grade of Damascus Steel Barrels that can be obtained" or "Whitworth Fluid Compressed Steel".
This is Bro. Tom's Grade 2 SAC; possibly a salesman's sample gun?
The right barrel has the "New Twist" pattern; but is roll-stamped "Improved Damascus". The left barrel is "Washington" and correct to grade.