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%I #2 Mar 30 2012 18:37:04
%S 1,2,4,8,12,20,32,52,72,104,156,228,332,436,592,820,1152,1588,2180,
%T 2772,3592,4744,6332,8512,11284,14876,18468,23212,29544,38056,49340,
%U 64216,82684,105896,129108,158652,196708,246048,310264,392948,498844,627952
%N First differences (A131771) equal this sequence with terms repeated at positions: {m*(m+1)/2, m>=0}.
%F a(n) = a(n-1) + a(n - t(n)) where t(n) = [(sqrt(8n + 17) - 3)/2] for n>0, with a(0)=1.
%e First differences (A131771) begin:
%e [1,1,2,4,4,8,12,20,20,32,52,72,104,104,156,228,332,436,592,592,...].
%e Second differences (A131772) begin:
%e [1,0,1,2,0,4,4,8,0,12,20,20,32,0,52,72,104,104,156,0,228,332,436,592,592,...]
%e which equals the first differences with zeros inserted at positions {m*(m+1)/2, m>=0}.
%o (PARI) a(n)=if(n==0,1,a(n-1)+a(n-(sqrtint(8*n+17)-3)\2))
%Y Cf. A131771 (first differences), A131772.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jul 14 2007
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