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 A068571 Number of happy numbers <= 10^n. 5
 1, 3, 20, 143, 1442, 14377, 143071, 1418854, 14255667, 145674808, 1492609148, 15091199357, 149121303586, 1443278000870, 13770853279685, 130660965862333, 1245219117260664, 12024696404768025, 118226055080025491, 1183229962059381238, 12005034444292997294 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS L. Klasen and Bryan Wolf, Table of n, a(n) for n = 0..1000 (first 122 terms from L. Klasen) Justin Gilmer, On the density of happy numbers (2011) L. Klasen, Xeen3d's happy.html W. Schneider, Happy Numbers Eric Weisstein's World of Mathematics, Happy Number FORMULA Contribution from Bryan Wolf, Nov 06 2012: (Begin) 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 Cf. A007770, A124095, A219667. Sequence in context: A082143 A009156 A074573 * A074569 A026303 A154627 Adjacent sequences:  A068568 A068569 A068570 * A068572 A068573 A068574 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

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