B737-300 DEPARTS WITH MISSING PAX SEAT BELT.

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FLT XXX; RNO TO SFO SCHEDULED XA15 DEP. PAPERWORK INDICATED NO OPEN OR DEFERRED MAINT WRITE-UPS. PREFLT ACTIVITIES ROUTINE (IE; BUSY). MY LEG; FIRST FLT OF A 5 LEG DAY. DEP BRIEFING LENGTHIER THAN NORMAL DUE TO COMPLICATED ENG FAILURE ON TKOF TERRAIN AVOIDANCE PROC AND HAVING A JUMP SEATER IN THE COCKPIT WHO REQUIRED BRIEFING. JUST MOMENTS BEFORE DEP THE LEAD FLT ATTENDANT HANDED THE WRITTEN COUNT OF ACFT OCCUPANTS TO OUR JUMP SEATER; WHO PLACED THE PAPER TOWEL ON THE CTR PEDESTAL; ALL WITHOUT COMMENT. RECEIVED OUR FINAL WT MANIFEST VIA ACARS AND LOOKED AT THE PAPER TOWEL TO VERIFY THE FLT ATTENDANT'S PAX NUMBER WITH THE STATION NUMBER. WHILE DOING SO; I NOTICED A NOTE ALSO WRITTEN ON THE TOWEL REGARDING 'SOMETHING NEEDED;' WHICH I BELIEVED TO BE CABIN SUPPLIES TO BE REQUESTED FROM OUR SFO STATION. PUSHBACK; ENG START AND TAXI NORMAL. DURING THE TAXI OUT; I LOOKED AT THE TOWEL AGAIN AND READ THE NOTE; 'NEED SEAT BELT SEAT XXX.' I MADE NOTE OF THIS MENTALLY; BELIEVING A SEAT BELT WAS DIRTY OR SOILED AND COULD USE REPLACING IN SFO. CLBOUT NORMAL. BEGAN CRUISE. AFTER OUR ROUTINE CRUISE ACTIVITIES WERE COMPLETE ON THE SHORT 31 MIN LEG; I MENTIONED TO THE CAPT THE NOTE AND THE APPARENT NEED TO HAVE A SEAT BELT REPLACED IN SFO. THE CAPT CONTACTED THE LEAD FLT ATTENDANT AND TO OUR SURPRISE; LEARNED THAT THE SEAT IN QUESTION HAD NO SEAT BELT WHATSOEVER. THE PROB IS THAT WE VIOLATED FARS BY NOT HAVING THE DISCREPANCY DECLARED AND ADDRESSED PRIOR TO PUSHBACK IN RNO. THE CAPT WROTE UP THE SEAT BELT ENRTE. ON THE GND IN SFO AND AFTER THE PAX AND JUMP SEATER HAD DEPLANED; THE CAPT SPOKE WITH THE LEAD FLT ATTENDANT. HE STATED THAT ACFT DISCREPANCIES NEED TO BE POSITIVELY VERBALIZED; NOT JUST WRITTEN. HE EXPLAINED HOW HE AND I HAD JUST VIOLATED FARS. THE FLT ATTENDANT MENTIONED THAT SOMEONE SHE BELIEVED TO BE A RNO MECH HAD MENTIONED THE LACK OF SEAT BELT TO HER IN RNO. THE CAPT ALSO CONTACTED RNO MAINT TO INVESTIGATE FURTHER. HUMAN PERFORMANCE CONSIDERATIONS CTR AROUND COMS. THE ERROR CHAIN BEGAN WITH RNO MAINT. THEY SHOULD HAVE NOTIFIED THE CAPT. THE FLT ATTENDANT SHOULD HAVE VERBALIZED THE WRITTEN NOTE. FURTHER; I SHOULD HAVE FULLY READ THE NOTE INITIALLY AND INQUIRED TO UNDERSTAND IT FULLY. I PERCEIVED THAT NEW ACFT PROBS WOULD BE VERBALIZED; NOT JUST WRITTEN. THE FLT ATTENDANT PERCEIVED THAT THE MECH HAD ALREADY SPOKEN TO US. CONTRIBUTING MIGHT HAVE BEEN THE EARLY HR RPTING TIME; THE LONG PREVIOUS DAY'S 7.3 HR; 4 LEGS WORTH OF FLYING; THE DELAY GETTING TO OUR ROOMS AT THE HOTEL; AND THE HIGH WORKLOAD INVOLVED WITH A FULL LOAD DEPARTING RNO TO THE S WITH A COMPLICATED ENG OUT PROC.