A081490 Leading term of n-th row of A081491.

1, 2, 4, 9, 19, 36, 62, 99, 149, 214, 296, 397, 519, 664, 834, 1031, 1257, 1514, 1804, 2129, 2491, 2892, 3334, 3819, 4349, 4926, 5552, 6229, 6959, 7744, 8586, 9487, 10449, 11474, 12564, 13721, 14947, 16244, 17614, 19059, 20581, 22182, 23864, 25629

Offset

1,2

Comments

First differences are given by A002522 = n^2 + 1. Second differences are odd numbers given by A005408.

a(1)=1, a(2)=2, (a(n+1) -a(n)) - (a(n) -a(n-1)) = 2*(n-1)-1. - Ben Paul Thurston, Aug 22 2009

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(1) = 1, a(n) = A081489(n-1) + 1.

From R. J. Mathar, Feb 06 2010: (Start)

G..f: x*(1-2*x+2*x^2+x^3)/(x-1)^4.

a(n) = n*(2*n^2 -9*n +19)/6 -1. (End)

a(n) = (n-2)^2 + a(n-1)+1, n>1. - Gary Detlefs, Jun 29 2010

a(1)=1, a(2)=2, a(3)=4, a(4)=9, a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4). - Harvey P. Dale, Apr 30 2011

Maple

with (combinat):a:=n->sum(fibonacci(3, i), i=0..n):seq(a(n)+1, n=-1..42); # Zerinvary Lajos, Apr 25 2008

Mathematica

Rest[CoefficientList[Series[x (1-2x+2x^2+x^3)/(x-1)^4, {x, 0, 50}], x]] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 2, 4, 9}, 50] (* Harvey P. Dale, Apr 30 2011 *)

Prog

(PARI) vector(50, n, (2*n^3-9*n^2+19*n-6)/6) \\ G. C. Greubel, Aug 13 2019
(Magma) [(2*n^3-9*n^2+19*n-6)/6: n in [1..50]]; // G. C. Greubel, Aug 13 2019
(Sage) [(2*n^3-9*n^2+19*n-6)/6 for n in (1..50)] # G. C. Greubel, Aug 13 2019
(GAP) List([1..50], n-> (2*n^3-9*n^2+19*n-6)/6); # G. C. Greubel, Aug 13 2019

Crossrefs

Cf. A002522, A005408, A081489, A081491, A081492.

Sequence in context: A368422 A283877 A331850 * A292478 A309267 A262864

Adjacent sequences: A081487 A081488 A081489 * A081491 A081492 A081493

Keyword

nonn,easy

Author

Amarnath Murthy, Mar 25 2003

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 29 2003

Status

approved