OFFSET
0,2
COMMENTS
The numbers in rows of the triangle are along skew diagonals pointing top-left in center-justified triangle in A303901 ((3-2x)^n).
The coefficients in the expansion of 1/(1-3x+2x^2) are given by the sequence generated by the row sums.
REFERENCES
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.
LINKS
Zagros Lalo, Left-justified triangle
EXAMPLE
Triangle begins:
.
n | k = 0 1 2 3 4 5 6
---+-----------------------------------------------------
0 | 1
1 | -2
2 | 4 3
3 | -8 -12
4 | 16 36 9
5 | -32 -96 -54
6 | 64 240 216 27
7 | -128 -576 -720 -216
8 | 256 1344 2160 1080 81
9 | -512 -3072 -6048 -4320 -810
10 | 1024 6912 16128 15120 4860 243
11 | -2048 -15360 -41472 -48384 -22680 -2916
12 | 4096 33792 103680 145152 90720 20412 729
13 | -8192 -73728 -253440 -414720 -326592 -108864 -10206
MATHEMATICA
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
PROG
(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)));
tabf(nn) = for (n=0, nn, for (k=0, n\2, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 10 2018
CROSSREFS
KEYWORD
tabf,easy,sign
AUTHOR
Zagros Lalo, May 04 2018
STATUS
approved