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A081490 Leading term of n-th row of A081491. 3
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..44.

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

FORMULA

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

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. - R. J. Mathar, Feb 06 2010

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)=4a(n-1)-6a(n-2)+4a(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

q=2; s=0; lst={1}; Do[s+=n^2; AppendTo[lst, s+n+q], {n, 0, 5!, 1}]; lst (* Vladimir Joseph Stephan Orlovsky, May 25 2009 *)

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

CROSSREFS

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

Sequence in context: A032175 A000678 A283877 * A292478 A262864 A129784

Adjacent sequences:  A081487 A081488 A081489 * A081491 A081492 A081493

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Mar 25 2003

EXTENSIONS

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

STATUS

approved

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Last modified May 23 12:38 EDT 2019. Contains 323514 sequences. (Running on oeis4.)