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A119726 Triangular array read by rows: T(n,1) = T(n,n) = 1, T(n,k) = 4*T(n-1, k-1) + 2*T(n-1, k).

%I A119726 #8 Sep 08 2022 08:45:25
%S A119726 1,1,1,1,6,1,1,16,26,1,1,36,116,106,1,1,76,376,676,426,1,1,156,1056,
%T A119726 2856,3556,1706,1,1,316,2736,9936,18536,17636,6826,1,1,636,6736,30816,
%U A119726 76816,109416,84196,27306,1,1,1276,16016,88576,276896,526096,606056,391396,109226,1
%N A119726 Triangular array read by rows: T(n,1) = T(n,n) = 1, T(n,k) = 4*T(n-1, k-1) + 2*T(n-1, k).
%C A119726 Second column is A048487.
%C A119726 Second diagonal is A020989.
%D A119726 TERMESZET VILAGA XI.TERMESZET-TUDOMANY DIAKPALYAZAT 133.EVF. 6.SZ. jun. 2002. Vegh Lea (and Vegh Erika): "Pascal-tipusu haromszogek" http://www.kfki.hu/chemonet/TermVil/tv2002/tv0206/tartalom.html
%H A119726 G. C. Greubel, <a href="/A119726/b119726.txt">Rows n = 1..100 of triangle, flattened</a>
%e A119726 Triangle begins as:
%e A119726   1;
%e A119726   1,    1;
%e A119726   1,    6,     1;
%e A119726   1,   16,    26,     1;
%e A119726   1,   36,   116,   106,      1;
%e A119726   1,   76,   376,   676,    426,      1;
%e A119726   1,  156,  1056,  2856,   3556,   1706,      1;
%e A119726   1,  316,  2736,  9936,  18536,  17636,   6826,      1;
%e A119726   1,  636,  6736, 30816,  76816, 109416,  84196,  27306,      1;
%e A119726   1, 1276, 16016, 88576, 276896, 526096, 606056, 391396, 109226, 1;
%p A119726 T:= proc(n, k) option remember;
%p A119726       if k=1 and k=n then 1
%p A119726     else 4*T(n-1, k-1) + 2*T(n-1, k)
%p A119726       fi
%p A119726 end: seq(seq(T(n, k), k=1..n), n=1..12); # _G. C. Greubel_, Nov 18 2019
%t A119726 T[n_, k_]:= T[n, k]= If[k==1 || k==n, 1, 4*T[n-1, k-1] + 2*T[n-1, k]]; Table[T[n,k], {n,10}, {k,n}]//Flatten (* _G. C. Greubel_, Nov 18 2019 *)
%o A119726 (PARI) T(n,k) = if(k==1 || k==n, 1, 4*T(n-1,k-1) + 2*T(n-1,k));
%o A119726 (Magma)
%o A119726 function T(n,k)
%o A119726   if k eq 1 or k eq n then return 1;
%o A119726   else return 4*T(n-1,k-1) + 2*T(n-1,k);
%o A119726   end if;
%o A119726   return T;
%o A119726 end function;
%o A119726 [T(n,k): k in [1..n], n in [1..12]]; // _G. C. Greubel_, Nov 18 2019
%o A119726 (Sage)
%o A119726 @CachedFunction
%o A119726 def T(n, k):
%o A119726     if (k==1 or k==n): return 1
%o A119726     else: return 4*T(n-1, k-1) + 2*T(n-1, k)
%o A119726 [[T(n, k) for k in (1..n)] for n in (1..12)] # _G. C. Greubel_, Nov 18 2019
%Y A119726 Cf. A007318, A020989, A048483, A048487, A119725, A119727, A123208.
%K A119726 easy,nonn,tabl
%O A119726 1,5
%A A119726 _Zerinvary Lajos_, Jun 14 2006
%E A119726 Edited by _Don Reble_, Jul 24 2006