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%I #22 Apr 03 2021 19:04:19
%S 0,0,1,0,1,3,1,4,11,5,16,41,22,63,155,92,247,591,376,967,2267,1518,
%T 3785,8735,6085,14820,33775,24285,58060,130965,96647,227612,509015,
%U 383911,892926,1982269,1523117,3505386,7732659,6037745,13770404,30208749
%N Sum along upward diagonal of Pascal triangle from (but not including) center.
%H David A. Corneth, <a href="/A010756/b010756.txt">Table of n, a(n) for n = 0..4992</a> (terms <= 10^1000)
%p A010756 := proc(d)
%p local a,n,m;
%p a := 0 ;
%p for n from 0 to d do
%p m := d-n ;
%p if m >= 1+floor(d/3) then
%p a := a+binomial(n,m) ;
%p end if;
%p end do:
%p a ;
%p end proc: # _R. J. Mathar_, Feb 08 2016
%t A010756[d_] := Module[{a, n, m}, a = 0; For[n = 0, n <= d, n++, m = d - n; If[m >= 1 + Floor[d/3], a = a + Binomial[n, m]]]; a]; Array[A010756, 42, 0] (* _Jean-François Alcover_, Dec 12 2016, after _R. J. Mathar_ *)
%o (PARI) a(n) = {if(n==0, return(0)); my(u = (2*n - 1)\3); sum(i = 1, u, binomial(i, n-i)) \\ _David A. Corneth_, Apr 03 2021
%Y Cf. A004396.
%K nonn
%O 0,6
%A _R. K. Guy_
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