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A178320 INVERT transform of A008805 (triangular numbers repeated). 0

%I

%S 1,2,6,14,35,85,208,508,1241,3032,7407,18096,44209,108005,263861,

%T 644625,1574849,3847430,9399452,22963302,56100424,137055967,334834156,

%U 818015548,1998450352,4882307945,11927707309,29139948412,71190260748

%N INVERT transform of A008805 (triangular numbers repeated).

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-2,-1,1).

%F G.f.: -1/(x^5-x^4-2*x^3+2*x^2+2*x-1).

%e a(3) = 14 = (3, 3, 1, 1) * (1, 1, 2, 6) = (3 + 3 + 2 + 6).

%p b:= proc(n) local m;

%p m:= ceil((n+1)/2);

%p m*(m+1)/2

%p end:

%p invtr:= proc(b)

%p local a;

%p a:= proc(n) option remember; local i;

%p `if`(n<1, 1, add(a(n-i) *b(i-1), i=1..n+1))

%p end;

%p end:

%p a:= invtr(b):

%p seq(a(n), n=0..30);

%t LinearRecurrence[{2, 2, -2, -1, 1}, {1, 2, 6, 14, 35}, 30] (* _Jean-Fran├žois Alcover_, Nov 28 2020 *)

%Y Cf. A008805.

%K nonn,easy

%O 0,2

%A _Gary W. Adamson_, Dec 21 2010

%E Edited by _Alois P. Heinz_, Dec 25 2010

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Last modified April 11 03:12 EDT 2021. Contains 342886 sequences. (Running on oeis4.)