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A131075 First subdiagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 8) < 4, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j.

%I A131075 #9 Jan 29 2025 07:53:06
%S A131075 1,2,4,7,11,16,22,30,46,92,232,628,1652,4096,9544,21000,43912,87824,
%T A131075 169120,315952,578096,1048576,1913440,3567072,6874336,13748672,
%U A131075 28384384,59797312,126906176,268435456,561834112,1158971520,2353246336,4706492672,9292452352
%N A131075 First subdiagonal of triangular array T: T(j,1) = 1 for ((j-1) mod 8) < 4, else 0; T(j,k) = T(j-1,k-1) + T(j,k-1) for 2 <= k <= j.
%C A131075 Also first differences of main diagonal A129961.
%H A131075 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-10,4).
%F A131075 a(1) = 1, a(2) = 2, a(3) = 4, a(4) = 7, a(5) = 11; for n > 5, a(n) = 6*a(n-1)-14*a(n-2)+16*a(n-3)-10*a(n-4)+4*a(n-5).
%F A131075 G.f.: x*(1-4*x+6*x^2-5*x^3+3*x^4)/((1-2*x)*(1-4*x+6*x^2-4*x^3+2*x^4)).
%e A131075 For first seven rows of T see A131074 or A129961.
%o A131075 (Magma) m:=34; M:=ZeroMatrix(IntegerRing(), m, m); for j:=1 to m do if (j-1) mod 8 lt 4 then M[j, 1]:=1; end if; end for; for k:=2 to m do for j:=k to m do M[j, k]:=M[j-1, k-1]+M[j, k-1]; end for; end for; [ M[n+1, n]: n in [1..m-1] ];
%o A131075 (PARI) lista(m) = my(v=concat([1, 2, 4, 7, 11], vector(m-5))); for(n=6, m, v[n]=6*v[n-1]-14*v[n-2]+16*v[n-3]-10*v[n-4]+4*v[n-5]); v
%Y A131075 Cf. A131074 (T read by rows), A129961 (main diagonal of T), A131076 (row sums of T), A131077 (antidiagonal sums of T). First through sixth column of T are in A131078, A131079, A131080, A131081, A131082, A131083 resp.
%K A131075 nonn,easy
%O A131075 1,2
%A A131075 _Klaus Brockhaus_, following a suggestion of _Paul Curtz_, Jun 14 2007