

A110325


Row sums of number triangle related to the Jacobsthal numbers.


3



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
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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!)/(1a*xb*x^2) have g.f. (1(a+2)x(2ba1)x^2)/(1x)^3 and general term 1+(ba)*nb*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.: (13*x2*x^2)/(1x)^3.
a(n) = 3*a(n1) 3*a(n2) +a(n3).  Vincenzo Librandi, Jul 08 2012


MATHEMATICA

CoefficientList[Series[(13x2x^2)/(1x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)


PROG

(MAGMA) [1+n2*n^2: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012
(PARI) a(n)=1+n2*n^2 \\ Charles R Greathouse IV, Jun 17 2017


CROSSREFS

Cf. A014106 (essentially the same sequence).
Sequence in context: A065351 A002503 A014106 * A140342 A055454 A301294
Adjacent sequences: A110322 A110323 A110324 * A110326 A110327 A110328


KEYWORD

easy,sign


AUTHOR

Paul Barry, Jul 20 2005


STATUS

approved



