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A081490
Leading term of n-th row of A081491.
4
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
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
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
Sequence in context: A283877 A331850 A373808 * A292478 A309267 A262864
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

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Last modified September 20 06:27 EDT 2024. Contains 376052 sequences. (Running on oeis4.)