0,2

The number of digits approximately doubles moving to the next member in the sequence; therefore a(8) onwards are not shown. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 09 2008

J. V. Post, "Iterated Polygonal Numbers", preprint.

J. V. Post, "Iterated Triangular Numbers", preprint.

Eric Weisstein's World of Mathematics, "Heptagonal Number."

a(0, n) = 1. a(1, n) = Hep(n) = the n-th heptagonal number = n*(5*n-3)/2. a(2, n) = Hep(Hep(n)) = the Hep(n)th heptagonal number = [n*(5*n-3)/2]*{5*n*(5*n-3)/2-3}/2 = (1/4)*{[Hep(n)]^2 - 3*Hep(n)}. a(3, n) = Hep(Hep(Hep(n)))) = (1/8)*{125*[Hep(n)]^4 - 90*[Hep(n)]^3 + 9*[Hep(n)]^2} = (1/8)*{78125*n^8 - 187500*n^7 + 150000*n^6 - 33750*n^5 - 9375*n^4 + 3150*n^3 + 315*n^2 - 27*n}. In general, a(k+1, n) = Hep[a(k, n)] = a(k, n)* [5*a(k, n)-3]/2.

a(n)= A000566(a(n-1)), n>1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 09 2008

a(3) = 31192 because a(1) = the first heptagonal number = 7; a(2) = the 7th heptagonal number = 7*(5*7-3)/2 = 112; a(3) = the 112th heptagonal number = 112*(5*112-3)/2 = 31192.

Cf. A007501, A000566.

Sequence in context: A128576 A147631 A010795 this_sequence A079296 A081531 A142537

Adjacent sequences: A099150 A099151 A099152 this_sequence A099154 A099155 A099156

easy,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Nov 15 2004

Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 09 2008