OFFSET
0,2
COMMENTS
The numbers in rows of the triangle are along skew diagonals pointing top-right in center-justified triangle given in A303901 ((3-2x)^n).
Row n gives coefficients of Fermat polynomial.
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, 104, 394, 395.
LINKS
Zagros Lalo, Left-justified triangle
Eric Weisstein's World of Mathematics, Fermat Polynomial.
EXAMPLE
Triangle begins:
n\k | 0 1 2 3 4 5 6 7
----+--------------------------------------------------------------------
0| 1
1| 3
2| 9 -2
3| 27 -12
4| 81 -54 4
5| 243 -216 36
6| 729 -810 216 -8
7| 2187 -2916 1080 -96
8| 6561 -10206 4860 -720 16
9| 19683 -34992 20412 -4320 240
10| 59049 -118098 81648 -22680 2160 -32
11| 177147 -393660 314928 -108864 15120 -576
12| 531441 -1299078 1180980 -489888 90720 -6048 64
13| 1594323 -4251528 4330260 -2099520 489888 -48384 1344
14| 4782969 -13817466 15588936 -8660520 2449440 -326592 16128 -128
15|14348907 -44641044 55269864 -34642080 11547360 -1959552 145152 -3072
MATHEMATICA
t[0, 0] = 1; t[n_, k_] := If[n < 0 || k < 0, 0, 3 t[n - 1, k] - 2 t[n - 2, k - 1]]; Table[t[n, k], {n, 0, 14}, {k, 0, Floor[n/2]}] // Flatten
PROG
(PARI) T(n, k) = if ((n<0) || (k<0), 0, if ((n==0) && (k==0), 1, 3*T(n-1, k) - 2*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 03 2018
STATUS
approved