%I A131770
%S A131770 1,2,4,8,12,20,32,52,72,104,156,228,332,436,592,820,1152,1588,2180,2772,
%T A131770 3592,4744,6332,8512,11284,14876,18468,23212,29544,38056,49340,64216,
%U A131770 82684,105896,129108,158652,196708,246048,310264,392948,498844,627952
%N A131770 First differences (A131771) equal this sequence with terms repeated at 
               positions: {m*(m+1)/2, m>=0}.
%F A131770 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 A131770 First differences (A131771) begin:
%e A131770 [1,1,2,4,4,8,12,20,20,32,52,72,104,104,156,228,332,436,592,592,...].
%e A131770 Second differences (A131772) begin:
%e A131770 [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 A131770 which equals the first differences with zeros inserted at positions {m*(m+1)/
               2, m>=0}.
%o A131770 (PARI) a(n)=if(n==0,1,a(n-1)+a(n-(sqrtint(8*n+17)-3)\2))
%Y A131770 Cf. A131771 (first differences), A131772.
%Y A131770 Sequence in context: A023598 A103258 A100684 this_sequence A163489 A076651 
               A081410
%Y A131770 Adjacent sequences: A131767 A131768 A131769 this_sequence A131771 A131772 
               A131773
%K A131770 nonn
%O A131770 0,2
%A A131770 Paul D. Hanna (pauldhanna(AT)juno.com), Jul 14 2007