A110325 Row sums of number triangle related to the Jacobsthal numbers.

1, 0, -5, -14, -27, -44, -65, -90, -119, -152, -189, -230, -275, -324, -377, -434, -495, -560, -629, -702, -779, -860, -945, -1034, -1127, -1224, -1325, -1430, -1539, -1652, -1769, -1890, -2015, -2144, -2277, -2414, -2555, -2700, -2849, -3002, -3159, -3320, -3485, -3654, -3827, -4004, -4185, -4370

Offset

0,3

Comments

Essentially the same sequence as A014106.

Rows sums of A110324. Results from a general construction: the row sums of the inverse of the number triangle whose columns have e.g.f. (x^k/k!)/(1-a*x-b*x^2) have g.f. (1-(a+2)x-(2b-a-1)x^2)/(1-x)^3 and general term 1+(b-a)*n-b*n^2. This is the binomial transform of (1,-a,-2b,0,0,0,...).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 1 + n - 2*n^2.

G.f.: (1-3*x-2*x^2)/(1-x)^3.

a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - Vincenzo Librandi, Jul 08 2012

Mathematica

CoefficientList[Series[(1-3x-2x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)

Prog

(Magma) [1+n-2*n^2: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012
(PARI) a(n)=1+n-2*n^2 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A014106 (essentially the same sequence).

Sequence in context: A065351 A002503 A014106 * A331775 A140342 A055454

Adjacent sequences: A110322 A110323 A110324 * A110326 A110327 A110328

Keyword

easy,sign

Author

Paul Barry, Jul 20 2005

Status

approved