A059406 - OEIS

%I #17 Feb 19 2024 10:29:44

%S 1,2,7,77,8932,119675402,21483302825630107,

%T 692298450446589820159203790062227,

%U 718915716736124071145150312487360788973317227637596552328693330407

%N a(n) = a(n-1)*(3a(n-1) + 1)/2 with a(1) = 1.

%C a(1) = 1, a(n+1) = sum of a(n) numbers beginning with a(n) + 1: a(2) = 2, a(3) = 3+4 = 7, a(4) = 8+9+...13+14 = 77. - _Amarnath Murthy_, Sep 07 2005

%H Harry J. Smith, <a href="/A059406/b059406.txt">Table of n, a(n) for n = 1..12</a>

%F a(n) = A007501(n)/3 = A005449(a(n-1)). - _Henry Bottomley_, Oct 03 2001

%e a(3) = 7 so a(4) = 7*(3*7 + 1)/2 = 7*22/2 = 77.

%t f[n_Integer] := n(3n + 1)/2; NestList[f, 2, 8]

%o (PARI) { a=2/3; for (n = 1, 12, write("b059406.txt", n, " ", a=a*(3*a + 1)/2); ) } \\ _Harry J. Smith_, Jun 26 2009

%Y Cf. A000326.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Jan 29 2001