A119303 Expansion of (1 - 3x)/(1 - x + 2x^2 - x^3).

1, -2, -4, 1, 7, 1, -12, -7, 18, 20, -23, -45, 21, 88, 1, -154, -68, 241, 223, -327, -532, 345, 1082, -140, -1959, -597, 3181, 2416, -4543, -6194, 5308, 13153, -3657, -24655, -4188, 41465, 25186, -61932, -70839, 78211, 157957, -69304, -307007, -10442, 534268

Offset: 0

Author

Paul Barry, May 13 2006

Keywords

• easy
• sign

Comments

Row sums of number triangle A119302.

Links

• Index entries for linear recurrences with constant coefficients, signature (1,-2,1).

Programs

Mathematica

RecurrenceTable[{a[0]==1, a[1]== -2, a[2]== -4, a[n]== a[n-1] - 2*a[n-2] + a[n-3]}, a, {n,30}] (* G. C. Greubel, Aug 07 2015 *)
LinearRecurrence[{1,-2,1},{1,-2,-4},50] (* Harvey P. Dale, Oct 11 2019 *)

Formula

a(n) = a(n-1) - 2a(n-2) + a(n-3);

a(n) = Sum_{k=0..n} (C(2k, n-k) + 3*C(2k, n-k-1))*(-1)^(n-k).