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A176483 Triangle, read by rows, defined by T(n, k) = b(n) - b(k) - b(n-k) + 1, where b(n) = 5*b(n-1) - 4*b(n-2) + 3*b(n-3) - 2*b(n-4) - b(n-5) and b(0) = 0, b(1) = 1, b(2) = 5, b(3) = 21, b(4) = 88.

%I A176483 #13 May 07 2019 17:38:24
%S A176483 1,1,1,1,4,1,1,16,16,1,1,67,79,67,1,1,281,344,344,281,1,1,1176,1453,
%T A176483 1504,1453,1176,1,1,4921,6093,6358,6358,6093,4921,1,1,20594,25511,
%U A176483 26671,26885,26671,25511,20594,1,1,86185,106775,111680,112789,112789,111680,106775,86185,1
%N A176483 Triangle, read by rows, defined by T(n, k) = b(n) - b(k) - b(n-k) + 1, where  b(n) = 5*b(n-1) - 4*b(n-2) + 3*b(n-3) - 2*b(n-4) - b(n-5) and b(0) = 0, b(1) = 1, b(2) = 5, b(3) = 21, b(4) = 88.
%C A176483 Row sums are {1, 2, 6, 34, 215, 1252, 6764, 34746, 172439, 834860, 3967727, ...}.
%H A176483 Indranil Ghosh, <a href="/A176483/b176483.txt">Rows 0..120, flattened</a>
%H A176483 Indranil Ghosh, <a href="/A176483/a176483.txt">Python Program to generate the b-file</a>
%F A176483 Let b(n) = 5*b(n-1) - 4*b(n-2) + 3*b(n-3) - 2*b(n-4) - b(n-5), with b(0) = 0, b(1) = 1, b(2) = 5, b(3) = 21, b(4) = 88, then T(n, k) = b(n) - b(k) - b(n-k) + 1.
%e A176483 Triangle begins as:
%e A176483   1;
%e A176483   1,     1;
%e A176483   1,     4,      1;
%e A176483   1,    16,     16,      1;
%e A176483   1,    67,     79,     67,      1;
%e A176483   1,   281,    344,    344,    281,      1;
%e A176483   1,  1176,   1453,   1504,   1453,   1176,      1;
%e A176483   1,  4921,   6093,   6358,   6358,   6093,   4921,      1;
%e A176483   1, 20594,  25511,  26671,  26885,  26671,  25511,  20594,     1;
%e A176483   1, 86185, 106775, 111680, 112789, 112789, 111680, 106775, 86185, 1;
%e A176483 ...
%e A176483 T(3,2) = b(3) - b(2) - b(3 - 2) + 1 = 21 - 5 - 1 + 1 = 16 [b(1) = 1, b(2) = 5, b(3) = 21]. - _Indranil Ghosh_, Feb 17 2017
%t A176483 b[0]:=0; b[1]:=1; b[2]:=5; b[3]:=21; b[4]:=88;
%t A176483 b[n_]:= 5*b[n-1] -4*b[n-2] +3*b[n-3] -2*b[n-4] -b[n-5];
%t A176483 T[n_, m_]:= b[n] -b[m] -b[n-m] +1;
%t A176483 Table[T[n, m], {n,0,10}, {m,0,n}]//Flatten (* modified by _G. C. Greubel_, May 06 2019 *)
%o A176483 (PARI)
%o A176483 {b(n) = if(n==0, 0, if(n==1, 1, if(n==2, 5, if(n==3, 21, if(n==4, 88, 5*b(n-1) -4*b(n-2) +3*b(n-3) -2*b(n-4) -b(n-5))))))};
%o A176483 {T(n, k) = b(n) -b(k) -b(n-k) +1};
%o A176483 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 06 2019
%o A176483 (Sage)
%o A176483 def b(n):
%o A176483     if (n==0): return 0
%o A176483     elif (n==1): return 1
%o A176483     elif (n==2): return 5
%o A176483     elif (n==3): return 21
%o A176483     elif (n==4): return 88
%o A176483     else: return 5*b(n-1) -4*b(n-2) +3*b(n-3) -2*b(n-4) -b(n-5)
%o A176483 def T(n, k): return b(n) - b(k) - b(n-k) + 1
%o A176483 [[T(n, k) for k in (0..n)] for n in (0..12)] # _G. C. Greubel_, May 06 2019
%Y A176483 Cf. A095263.
%K A176483 nonn,tabl
%O A176483 0,5
%A A176483 _Roger L. Bagula_, Apr 18 2010
%E A176483 Edited by _G. C. Greubel_, May 06 2019