%I #26 Dec 12 2015 15:42:02
%S 1,2,10,30,111,296,711,1625,3583,7088,13377,24143,41376,68551,111068,
%T 174887,269592,410043,612350,900484,1310108,1879862,2664399,3740002,
%U 5188376,7121305,9687674,13044961,17402217,23026128,30200375,39290567,50744867,65045752,82799083
%N Number of happy numbers without zeros and with digits in nondecreasing order <= 10^n.
%H Bryan Wolf, <a href="/A219667/b219667.txt">Table of n, a(n) for n = 0..10000</a>
%H Bryan Wolf, <a href="/A219667/a219667.cpp.txt">C++ program for generating n, a(n)</a>
%F h(d,n,x) = h(d-1,n-x^2,x) + h(d-1,n-(x+1)^2,x+1) + ... + h(n-1,n-9^2,9) where h() is the number of d-digit long happy numbers with digits in nondecreasing order,
%F n is the sum of the squares of the digits in the happy numbers, and x is the lowest digit in the happy numbers.
%F a(n) is the sum of all h(d,0 <= x <= 81*d, 1), where x is a happy number.
%e h(0, 0, 1 <= x <= 9) = 1,
%e h(d, n, x) = 0 for all n < 0,
%e h(d, n, x) = 0 for all n > 81*d.
%Y Cf. A007770, A068571, A124095.
%K base,nonn
%O 0,2
%A _Bryan Wolf_, Nov 30 2012