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

Author

Amarnath Murthy, Mar 25 2003

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

GAP

List([1..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

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 *)

PARI

vector(50, n, (2*n^3-9*n^2+19*n-6)/6) \\ 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

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

Extensions

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