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A178320 INVERT transform of A008805 (triangular numbers repeated).

%I A178320 #17 Nov 28 2020 09:09:22
%S A178320 1,2,6,14,35,85,208,508,1241,3032,7407,18096,44209,108005,263861,
%T A178320 644625,1574849,3847430,9399452,22963302,56100424,137055967,334834156,
%U A178320 818015548,1998450352,4882307945,11927707309,29139948412,71190260748
%N A178320 INVERT transform of A008805 (triangular numbers repeated).
%H A178320 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A178320 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2,-1,1).
%F A178320 G.f.: -1/(x^5-x^4-2*x^3+2*x^2+2*x-1).
%e A178320 a(3) = 14 = (3, 3, 1, 1) * (1, 1, 2, 6) = (3 + 3 + 2 + 6).
%p A178320 b:= proc(n) local m;
%p A178320   m:= ceil((n+1)/2);
%p A178320   m*(m+1)/2
%p A178320 end:
%p A178320 invtr:= proc(b)
%p A178320   local a;
%p A178320   a:= proc(n) option remember; local i;
%p A178320         `if`(n<1, 1, add(a(n-i) *b(i-1), i=1..n+1))
%p A178320   end;
%p A178320 end:
%p A178320 a:= invtr(b):
%p A178320 seq(a(n), n=0..30);
%t A178320 LinearRecurrence[{2, 2, -2, -1, 1}, {1, 2, 6, 14, 35}, 30] (* _Jean-François Alcover_, Nov 28 2020 *)
%Y A178320 Cf. A008805.
%K A178320 nonn,easy
%O A178320 0,2
%A A178320 _Gary W. Adamson_, Dec 21 2010
%E A178320 Edited by _Alois P. Heinz_, Dec 25 2010