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%I #9 Apr 24 2016 08:32:14
%S 1,4,9,10,16,25,27,36,49,52,64,81,85,100,121,126,144,169,175,196,225,
%T 232,256,289,297,324,361,370,400,441,451,484,529,540,576,625,637,676,
%U 729,742,784,841,855,900,961,976,1024,1089,1105,1156,1225,1242,1296
%N The union of squares (A000290) and 10-gonal numbers (A001107).
%H Colin Barker, <a href="/A272266/b272266.txt">Table of n, a(n) for n = 1..1000</a>
%F Conjectures:
%F a(n) = a(n-1)+2*a(n-3)-2*a(n-4)-a(n-6)+a(n-7) for n>7.
%F G.f. x*(1+3*x+5*x^2-x^3-x^5+x^6) / ((1-x)^3*(1+x+x^2)^2).
%o (PARI)
%o pg(m, n) = (n^2*(m-2)-n*(m-4))/2 \\ The n-th m-gonal number
%o pgr(m, r) = n=1; L=List(); while((t=pg(m, n))<r, listput(L, t); n++); Vec(L)
%o pgpgs(p, q, r) = setunion(pgr(p, r), pgr(q, r))
%o pgpgs(4, 10, 2000)
%Y Cf. A000290, A001107, A272267.
%K nonn
%O 1,2
%A _Colin Barker_, Apr 24 2016
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