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A304213 Triangle read by rows: T(0,0) = 1; T(n,k) = 2*T(n-1,k) - 2*T(n-2,k-1) + T(n-3,k-2) for k = 0..floor(2*n/3); T(n,k)=0 for n or k < 0. 1
1, 2, 4, -2, 8, -8, 1, 16, -24, 8, 32, -64, 36, -4, 64, -160, 128, -32, 1, 128, -384, 400, -160, 18, 256, -896, 1152, -640, 136, -6, 512, -2048, 3136, -2240, 720, -80, 1, 1024, -4608, 8192, -7168, 3120, -592, 32, 2048, -10240, 20736, -21504, 11872, -3264, 360, -8, 4096, -22528, 51200, -61440, 41216, -15008, 2624, -160, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The numbers in rows of the triangle are along skew diagonals pointing top-right in center-justified triangle given in A304209.

The coefficients in the expansion of 1/(1-2*x+2*x^2-x^3) 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. 204, 205.

LINKS

Table of n, a(n) for n=0..60.

Shara Lalo, Left-justified triangle

EXAMPLE

Triangle begins:

      1;

      2;

      4,      -2;

      8,      -8,      1;

     16,     -24,      8;

     32,     -64,     36,      -4;

     64,    -160,    128,     -32,      1;

    128,    -384,    400,    -160,     18;

    256,    -896,   1152,    -640,    136,      -6;

    512,   -2048,   3136,   -2240,    720,     -80,     1;

   1024,   -4608,   8192,   -7168,   3120,    -592,    32;

   2048,  -10240,  20736,  -21504,  11872,   -3264,   360,     -8;

   4096,  -22528,  51200,  -61440,  41216,  -15008,  2624,   -160,   1;

   8192,  -49152, 123904, -168960, 133632,  -60928, 14896,  -1632,  50;

  16384, -106496, 294912, -450560, 410880, -225792, 71680, -11776, 780, -10;

  ...

PROG

(PARI) T(n, k) = if ((n<0) || (k<0), 0, if ((n==0) && (k==0), 1, 2*T(n-1, k)-2*T(n-2, k-1)+T(n-3, k-2)));

tabf(nn) = for (n=0, nn, for (k=0, 2*n\3, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 10 2018

CROSSREFS

Row sums is similar to A021823.

Cf. A304209.

Sequence in context: A278221 A287879 A336093 * A129178 A152874 A324716

Adjacent sequences:  A304210 A304211 A304212 * A304214 A304215 A304216

KEYWORD

tabf,easy,sign

AUTHOR

Shara Lalo, May 08 2018

STATUS

approved

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Last modified May 16 00:49 EDT 2021. Contains 343937 sequences. (Running on oeis4.)