login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS").
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A091005 Expansion of x^2/((1-2*x)*(1+3*x)). 5
0, 0, 1, -1, 7, -13, 55, -133, 463, -1261, 4039, -11605, 35839, -105469, 320503, -953317, 2876335, -8596237, 25854247, -77431669, 232557151, -697147165, 2092490071, -6275373061, 18830313487, -56482551853, 169464432775, -508359743893, 1525146340543 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Inverse binomial transform of A091002.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

FORMULA

2^n = A091003(n) + 3*A091004(n) + 6*a(n).

a(n) = (3*2^n + 2*(-3)^n - 5*0^n)/30.

E.g.f.: (3*exp(2*x) + 2*exp(-3*x) - 5)/30. - G. C. Greubel, Feb 01 2019

MATHEMATICA

a[n_]:=(MatrixPower[{{1, 4}, {1, -2}}, n].{{1}, {1}})[[2, 1]]; Table[a[n], {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)

Join[{0, 0}, LinearRecurrence[{-1, 6}, {1, -1}, 30]] (* G. C. Greubel, Feb 01 2019 *)

PROG

(PARI) vector(30, n, n--; (3*2^n + 2*(-3)^n - 5*0^n)/30) \\ G. C. Greubel, Feb 01 2019

(MAGMA) [0] cat [(3*2^n + 2*(-3)^n)/30: n in [1..30]]; // G. C. Greubel, Feb 01 2019

(Sage) [0] + [(3*2^n + 2*(-3)^n)/30 for n in (1..30)] # G. C. Greubel, Feb 01 2019

(GAP) Concatenation([0], List([1..30], n -> (3*2^n + 2*(-3)^n)/30)) # G. C. Greubel, Feb 01 2019

CROSSREFS

Cf. A015441.

Sequence in context: A018562 A112540 A193489 * A015441 A255286 A253210

Adjacent sequences:  A091002 A091003 A091004 * A091006 A091007 A091008

KEYWORD

easy,sign

AUTHOR

Paul Barry, Dec 13 2003

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 November 27 15:11 EST 2020. Contains 338683 sequences. (Running on oeis4.)