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A302747 Triangle read by rows: T(0,0) = 1; T(n,k) = -2*T(n-1,k) + 3*T(n-2,k-1) for 0 <= k <= floor(n/2); T(n,k)=0 for n or k < 0.

%I A302747 #51 Sep 01 2018 10:17:06
%S A302747 1,-2,4,3,-8,-12,16,36,9,-32,-96,-54,64,240,216,27,-128,-576,-720,
%T A302747 -216,256,1344,2160,1080,81,-512,-3072,-6048,-4320,-810,1024,6912,
%U A302747 16128,15120,4860,243,-2048,-15360,-41472,-48384,-22680,-2916,4096,33792,103680,145152,90720,20412,729,-8192,-73728,-253440
%N A302747 Triangle read by rows: T(0,0) = 1; T(n,k) = -2*T(n-1,k) + 3*T(n-2,k-1) for 0 <= k <= floor(n/2); T(n,k)=0 for n or k < 0.
%C A302747 The numbers in rows of the triangle are along skew diagonals pointing top-left in center-justified triangle in A303901 ((3-2x)^n).
%C A302747 The coefficients in the expansion of 1/(1-3x+2x^2) are given by the sequence generated by the row sums.
%D A302747 Shara Lalo and Zagros Lalo, Polynomial Expansion Theorems and Number Triangles, Zana Publishing, 2018, ISBN: 978-1-9995914-0-3, pp. 70, 72, 394-396.
%H A302747 Zagros Lalo, <a href="/A302747/a302747.pdf">Left-justified triangle</a>
%e A302747 Triangle begins:
%e A302747 .
%e A302747    n | k = 0      1       2       3       4       5       6
%e A302747   ---+-----------------------------------------------------
%e A302747    0 |     1
%e A302747    1 |    -2
%e A302747    2 |     4      3
%e A302747    3 |    -8    -12
%e A302747    4 |    16     36       9
%e A302747    5 |   -32    -96     -54
%e A302747    6 |    64    240     216      27
%e A302747    7 |  -128   -576    -720    -216
%e A302747    8 |   256   1344    2160    1080      81
%e A302747    9 |  -512  -3072   -6048   -4320    -810
%e A302747   10 |  1024   6912   16128   15120    4860     243
%e A302747   11 | -2048 -15360  -41472  -48384  -22680   -2916
%e A302747   12 |  4096  33792  103680  145152   90720   20412     729
%e A302747   13 | -8192 -73728 -253440 -414720 -326592 -108864  -10206
%t A302747 t[0, 0] = 1; t[n_, k_] := If[n < 0 || k < 0, 0, -2 t[n - 1, k] + 3 t[n - 2, k - 1]]; Table[t[n, k], {n, 0, 13}, {k, 0, Floor[n/2]}] // Flatten
%o A302747 (PARI) T(n,k) = if ((n<0) || (k<0), 0, if ((n==0) && (k==0), 1, -2*T(n-1,k) + 3*T(n-2,k-1)));
%o A302747 tabf(nn) = for (n=0, nn, for (k=0, n\2, print1(T(n,k), ", ")); print); \\ _Michel Marcus_, May 10 2018
%Y A302747 Row sums give A014983.
%Y A302747 Cf. A303901, A303941.
%K A302747 tabf,easy,sign
%O A302747 0,2
%A A302747 _Zagros Lalo_, May 04 2018