OFFSET
0,2
LINKS
Bryan Wolf, Table of n, a(n) for n = 0..1000 (first 122 terms from Lambert Klasen)
Justin Gilmer, On the density of happy numbers, arXiv:1110.3836 [math.NT], 2011-2015.
Lambert Klasen, Xeen3d's happy.html.
Walter Schneider, Happy Numbers.
Eric Weisstein's World of Mathematics, Happy Number.
FORMULA
From Bryan Wolf, Nov 06 2012: (Start)
h(n,x) = h(n-1,x-0^2) + h(n-1,x-1^2) + ... + h(n-1,x-9^2) where h() is the number of numbers of length n whose sum of the squares of their digits is x.
a(n) is the sum of all h(n, 0 < x <= 81*n), where x is a happy number, plus 1 for 10^n. (End)
EXAMPLE
For n=0, h(0,0) = 1 and h(0,x >0) = 0.
PROG
(PARI) ssd(n)=n=digits(n); sum(i=1, #n, n[i]^2)
happy(n)=while(n>6, n=ssd(n)); n==1
a(n)=my(f=n!, s, d); forvec(v=vector(9, i, [0, n]), d=vector(9, i, if(i>8, n, v[i+1])-v[i]); if(happy(sum(i=1, 9, d[i]*i^2)), s+=f/prod(i=1, 9, d[i]!)/v[1]!), 1); s+1 \\ Charles R Greathouse IV, Nov 01 2016
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Sascha Kurz, Mar 26 2002
EXTENSIONS
More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.de), Nov 03 2004
STATUS
approved