On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers

<div>The <svg height="8.8423pt" id="M20" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 6.16729 8.8423" width="6.16729pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M442 569C442 628 407 660 362 660C328 660 292 648 255 616C200 568 165 508 123 334L106 264C80 242 52 222 23 202L30 176C54 191 76 205 100 222L87 166C73 103 79 43 95 19C108 0 139 -12 169 -12C242 -12 318 38 369 106L354 129C322 93 260 49 215 49C173 49 147 81 170 187L189 274C293 344 442 452 442 569ZM380 565C380 478 267 377 196 322L216 406C254 556 282 623 332 623C364 623 380 596 380 565Z" id="g113-127"></path></g></svg>th triangular number.</div>

International Journal of Mathematics and Mathematical Sciences

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Figure 1

Figure 1: On the Characterization and Enumeration of Some Generalized Trapezoidal Numbers 