Generalized Heptagonal Numbers
A generalized heptagonal number is obtained by the formula
where Tn is the nth triangular number. The first few generalized heptagonal numbers are:
- 1, 4, 7, 13, 18, 27, 34, 46, 55, 70, 81, 99, 112, … (sequence A085787 in OEIS)
Every other generalized heptagonal number is a regular heptagonal number. Besides 1 and 70, no generalized heptagonal numbers are also Pell numbers.
Read more about this topic: Heptagonal Number
Famous quotes containing the words generalized and/or numbers:
“One is conscious of no brave and noble earnestness in it, of no generalized passion for intellectual and spiritual adventure, of no organized determination to think things out. What is there is a highly self-conscious and insipid correctness, a bloodless respectability submergence of matter in manner—in brief, what is there is the feeble, uninspiring quality of German painting and English music.”
—H.L. (Henry Lewis)
“All experience teaches that, whenever there is a great national establishment, employing large numbers of officials, the public must be reconciled to support many incompetent men; for such is the favoritism and nepotism always prevailing in the purlieus of these establishments, that some incompetent persons are always admitted, to the exclusion of many of the worthy.”
—Herman Melville (1819–1891)