login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033453 "INVERT" transform of squares A000290. 270
1, 5, 18, 63, 221, 776, 2725, 9569, 33602, 117995, 414345, 1454992, 5109273, 17941453, 63002258, 221235399, 776878533, 2728045592, 9579660701, 33639430153, 118126444802, 414806579603, 1456612858961, 5114964721440, 17961439747441, 63072442405845, 221481854849938, 777743974335503, 2731084630047981 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of compositions of n+1 whose parts equal to q can be of q^2 kinds. Example: a(1)=5 because we have (2),(2'),(2"),(2'") and (1,1). Row sums of A105495. - Emeric Deutsch, Apr 10 2005

LINKS

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-2,1).

FORMULA

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

a(n) = 4*a(n-1) - 2*a(n-2) + a(n-3) for n>2. - Colin Barker, Mar 19 2019

MAPLE

read transforms; [seq(n^2, n=1..50)]; INVERT(%);

MATHEMATICA

nn=20; a=(x+x^2)/(1-x)^3; Drop[CoefficientList[Series[1/(1-a), {x, 0, nn}], x], 1]  (* Geoffrey Critzer, Aug 31 2012*)

PROG

(PARI) Vec((1 + x) / (1 - 4*x + 2*x^2 - x^3) + O(x^30)) \\ Colin Barker, Mar 19 2019

CROSSREFS

Cf. A105495.

Sequence in context: A111567 A121050 A029869 * A284840 A301749 A222373

Adjacent sequences:  A033450 A033451 A033452 * A033454 A033455 A033456

KEYWORD

nonn,changed

AUTHOR

N. J. A. Sloane.

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 13:29 EDT 2019. Contains 321330 sequences. (Running on oeis4.)