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%I #16 Jun 13 2015 00:51:32
%S 1,1,1,2,6,16,37,80,172,377,839,1874,4175,9274,20577,45665,101393,
%T 225193,500162,1110790,2466760,5477917,12164896,27015092,59993817,
%U 133231279,295872778,657057431,1459155634,3240410561,7196122817
%N Quadrisection of a generalized Padovan sequence.
%C Quadrisection of sequence with g.f. 1/(1 - x^3 - x^4), or A017817.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,5,-1).
%F G.f.: (1-x)^3/((1-x)^4-x^3).
%F a(n) = sum_{k=0..2n} binomial(k, 4n-3k).
%F a(n) = 4a(n-1) - 6a(n-2) + 5a(n-3) - a(n-4).
%F a(n) = A017817(4n).
%F a(n) = sum_{k=0..floor((n+1)/2)} binomial(n+k, 4k). - _Paul Barry_, May 09 2005
%t Join[{1},a=0;b=0;c=0;d=1;Table[a+=b;b+=c;c+=d;d+=a,{n,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2010 *)
%K easy,nonn
%O 0,4
%A _Paul Barry_, Sep 29 2004
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