鍘熺悊
銆銆浠(1)錛?,h(0)=1錛宑atalan鏁版弧瓚抽掑綊寮忥細銆銆h(n)= h(0)*h(n-1)+h(1)*h(n-2) + ... + h(n-1)h(0) (鍏朵腑n>=2)
銆銆鍙︾被閫掑綊寮忥細
銆銆h(n)=((4*n-2)/(n+1))*h(n-1);
銆銆璇ラ掓帹鍏崇郴鐨勮В涓猴細
銆銆h(n)=C(2n,n)/(n+1) (n=1,2,3,...)
銆銆鍗＄壒鍏版暟鐨勫簲鐢?br>銆銆錛堝疄璐ㄤ笂閮芥槸閫掑綊絳夊紡鐨勫簲鐢級
銆銆
鎷彿鍖栭棶棰?/h3>
銆銆鐭╅樀閾句箻錛?P=a1×a2×a3×……×an錛屼緷鎹箻娉曠粨鍚堝緥錛屼笉鏀瑰彉鍏墮『搴忥紝鍙敤鎷彿琛ㄧず鎴愬鐨勪箻縐紝璇曢棶鏈夊嚑縐嶆嫭鍙峰寲鐨勬柟妗堬紵(h(n)縐?
銆銆鍑烘爤嬈″簭闂
銆銆涓涓爤(鏃犵┓澶?鐨勮繘鏍堝簭鍒椾負1錛?錛?錛?#8230;錛宯錛屾湁澶氬皯涓笉鍚岀殑鍑烘爤搴忓垪?
銆銆鍒嗘瀽錛氬浜庢瘡涓涓暟鏉ヨ錛屽繀欏昏繘鏍堜竴嬈°佸嚭鏍堜竴嬈°傛垜浠妸榪涙爤璁句負鐘舵?#8216;1’錛屽嚭鏍堣涓虹姸鎬?#8216;0’銆俷涓暟鐨勬墍鏈夌姸鎬佸搴攏涓?鍜宯涓?緇勬垚鐨?n浣嶄簩榪涘埗鏁般傜敱浜庣瓑寰呭叆鏍堢殑鎿嶄綔鏁版寜鐓?鈥鐨勯『搴忔帓鍒椼佸叆鏍堢殑鎿嶄綔鏁癰澶т簬絳変簬鍑烘爤鐨勬搷浣滄暟a(a≤b)錛屽洜姝よ緭鍑哄簭鍒楃殑鎬繪暟鐩?鐢卞乏鑰屽彸鎵弿鐢眓涓?鍜宯涓?緇勬垚鐨?n浣嶄簩榪涘埗鏁幫紝1鐨勭瘡璁℃暟涓嶅皬浜?鐨勭瘡璁℃暟鐨勬柟妗堢鏁般?br>銆銆鍦?n浣嶄簩榪涘埗鏁頒腑濉叆n涓?鐨勬柟妗堟暟涓篶(2n,n),涓嶅～1鐨勫叾浣檔浣嶈嚜鍔ㄥ～0銆備粠涓噺鍘諱笉絎﹀悎瑕佹眰錛堢敱宸﹁屽彸鎵弿錛?鐨勭瘡璁℃暟澶т簬1鐨勭瘡璁℃暟錛夌殑鏂規鏁板嵆涓烘墍姹傘?br>銆銆涓嶇鍚堣姹傜殑鏁扮殑鐗瑰緛鏄敱宸﹁屽彸鎵弿鏃訛紝蹇呯劧鍦ㄦ煇涓濂囨暟浣?m+1浣嶄笂棣栧厛鍑虹幇m+1涓?鐨勭瘡璁℃暟鍜宮涓?鐨勭瘡璁℃暟錛屾鍚庣殑2(n-m)-1浣嶄笂鏈塶-m涓?1鍜宯-m-1涓?銆傚鑻ユ妸鍚庨潰榪?(n-m)-1浣嶄笂鐨?鍜?浜掓崲錛屼嬌涔嬫垚涓簄-m涓?鍜宯-m-1涓?錛岀粨鏋滃緱1涓敱n+1涓?鍜宯-1涓?緇勬垚鐨?n浣嶆暟錛屽嵆涓涓笉鍚堣姹傜殑鏁板搴斾簬涓涓敱n+1涓?鍜宯-1涓?緇勬垚鐨勬帓鍒椼?br>銆銆鍙嶈繃鏉ワ紝浠諱綍涓涓敱n+1涓?鍜宯-1涓?緇勬垚鐨?n浣嶄簩榪涘埗鏁幫紝鐢變簬0鐨勪釜鏁板2涓紝2n涓哄伓鏁幫紝鏁呭繀鍦ㄦ煇涓涓鏁頒綅涓婂嚭鐜?鐨勭瘡璁℃暟瓚呰繃1鐨勭瘡璁℃暟銆傚悓鏍峰湪鍚庨潰閮ㄥ垎0鍜?浜掓崲錛屼嬌涔嬫垚涓虹敱n涓?鍜宯涓?緇勬垚鐨?n浣嶆暟錛屽嵆n+1涓?鍜宯-1涓?緇勬垚鐨?n浣嶆暟蹇呭搴斾竴涓笉絎﹀悎瑕佹眰鐨勬暟銆?br>銆銆鍥犺屼笉鍚堣姹傜殑2n浣嶆暟涓巒錛?涓?錛宯錛?涓?緇勬垚鐨勬帓鍒椾竴涓瀵瑰簲銆?br>銆銆鏄劇劧錛屼笉絎﹀悎瑕佹眰鐨勬柟妗堟暟涓篶(2n,n+1)銆傜敱姝ゅ緱鍑?杈撳嚭搴忓垪鐨勬繪暟鐩?c(2n,n)-c(2n,n+1)=1/(n+1)*c(2n,n)銆?br>銆銆錛堣繖涓叕寮忕殑涓嬫爣鏄粠h(0)=1寮濮嬬殑錛?br>銆銆綾諱技錛氭湁2n涓漢鎺掓垚涓琛岃繘鍏ュ墽鍦恒傚叆鍦鴻垂5鍏冦傚叾涓彧鏈塶涓漢鏈変竴寮?鍏冮挒紲紝鍙﹀n浜哄彧鏈?0鍏冮挒紲紝鍓ч櫌鏃犲叾瀹冮挒紲紝闂湁澶氬皯涓柟娉曚嬌寰楀彧瑕佹湁10鍏冪殑浜轟拱紲紝鍞エ澶勫氨鏈?鍏冪殑閽炵エ鎵鵑浂錛?灝嗘寔5鍏冭呭埌杈捐浣滃皢5鍏冨叆鏍堬紝鎸?0鍏冭呭埌杈捐浣滀嬌鏍堜腑鏌?鍏冨嚭鏍?
銆銆鍑稿杈瑰艦鐨勪笁瑙掑墫鍒嗛棶棰?/h3>
銆銆
銆銆姹傚皢涓涓?a target="_blank" style="color: rgb(51, 102, 204); text-decoration: underline; ">鍑稿杈瑰艦鍖哄煙鍒嗘垚涓夎褰㈠尯鍩熺殑鏂規硶鏁般?br>銆銆綾諱技錛氫竴浣嶅ぇ鍩庡競鐨勫緥甯堝湪濂逛綇鎵浠ュ寳n涓鍖哄拰浠ヤ笢n涓鍖哄宸ヤ綔銆傛瘡澶╁ス璧?n涓鍖哄幓涓婄彮銆傚鏋滃ス浠庝笉絀胯秺錛堜絾鍙互紕板埌錛変粠瀹跺埌鍔炲叕瀹ょ殑瀵硅綰匡紝閭ｄ箞鏈夊灝戞潯鍙兘鐨勯亾璺紵
銆銆綾諱技錛氬湪鍦嗕笂閫夋嫨2n涓偣,灝嗚繖浜涚偣鎴愬榪炴帴璧鋒潵浣垮緱鎵寰楀埌鐨刵鏉＄嚎孌典笉鐩鎬氦鐨勬柟娉曟暟?
銆銆鐢ㄧ粰瀹氳妭鐐圭粍鎴愪簩鍙夋爲鐨勯棶棰?/h3>
銆銆
銆銆緇欏畾N涓妭鐐癸紝鑳芥瀯鎴愬灝戠涓嶅悓鐨?a target="_blank" style="color: rgb(51, 102, 204); text-decoration: underline; ">浜屽弶鏍?/a>錛?br>銆銆錛堣兘鏋勬垚h錛圢錛変釜錛?/span>
銆銆
銆銆姹傚皢涓涓?a target="_blank" style="color: rgb(51, 102, 204); text-decoration: underline; ">鍑稿杈瑰艦鍖哄煙鍒嗘垚涓夎褰㈠尯鍩熺殑鏂規硶鏁般?br>銆銆綾諱技錛氫竴浣嶅ぇ鍩庡競鐨勫緥甯堝湪濂逛綇鎵浠ュ寳n涓鍖哄拰浠ヤ笢n涓鍖哄宸ヤ綔銆傛瘡澶╁ス璧?n涓鍖哄幓涓婄彮銆傚鏋滃ス浠庝笉絀胯秺錛堜絾鍙互紕板埌錛変粠瀹跺埌鍔炲叕瀹ょ殑瀵硅綰匡紝閭ｄ箞鏈夊灝戞潯鍙兘鐨勯亾璺紵
銆銆綾諱技錛氬湪鍦嗕笂閫夋嫨2n涓偣,灝嗚繖浜涚偣鎴愬榪炴帴璧鋒潵浣垮緱鎵寰楀埌鐨刵鏉＄嚎孌典笉鐩鎬氦鐨勬柟娉曟暟?
銆銆
鐢ㄧ粰瀹氳妭鐐圭粍鎴愪簩鍙夋爲鐨勯棶棰?/h3>
銆銆
銆銆緇欏畾N涓妭鐐癸紝鑳芥瀯鎴愬灝戠涓嶅悓鐨?a target="_blank" style="color: rgb(51, 102, 204); text-decoration: underline; ">浜屽弶鏍?/a>錛?br>銆銆錛堣兘鏋勬垚h錛圢錛変釜錛?/span>
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