login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A084901 a(n) = 4^(n-2)*n*(5*n+3)/2. 5
0, 1, 13, 108, 736, 4480, 25344, 136192, 704512, 3538944, 17367040, 83623936, 396361728, 1853882368, 8573157376, 39258685440, 178241142784, 803158884352, 3594887626752, 15994458210304, 70781061038080, 311711546474496 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Binomial transform of A084900. Third binomial transform of heptagonal numbers A000566. Fourth binomial transform of (0,1,5,0,0,0,...).

Coefficients in the hypergeometric series identity 1 - 13*x/(x + 12) + 108*x*(x - 1)/((x + 12)*(x + 16)) - 736*x*(x - 1)*(x - 2)/((x + 12)*(x + 16)*(x + 20)) + ... = 0, valid in the half-plane Re(x) > 0. Cf. A276289 and A077616. - Peter Bala, May 30 2019

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (12,-48,64).

FORMULA

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

E.g.f.: x*(2 + 5*x)*exp(4*x)/2. - G. C. Greubel, Jun 06 2019

a(n) = 12*a(n-1)-48*a(n-2)+64*a(n-3). - Wesley Ivan Hurt, May 28 2021

MATHEMATICA

Table[2^(2*n-5)*n*(5*n+3), {n, 0, 30}] (* G. C. Greubel, Jun 06 2019 *)

LinearRecurrence[{12, -48, 64}, {0, 1, 13}, 30] (* or *) CoefficientList[ Series[-((x (1+x))/(-1+4 x)^3), {x, 0, 30}], x] (* Harvey P. Dale, Jul 14 2021 *)

PROG

(PARI) vector(30, n, n--; 2^(2*n-5)*n*(5*n+3)) \\ G. C. Greubel, Jun 06 2019

(Magma) [2^(2*n-5)*n*(5*n+3): n in [0..30]]; // G. C. Greubel, Jun 06 2019

(Sage) [2^(2*n-5)*n*(5*n+3) for n in (0..30)] # G. C. Greubel, Jun 06 2019

(GAP) List([0..30], n-> 2^(2*n-5)*n*(5*n+3)) # G. C. Greubel, Jun 06 2019

CROSSREFS

Cf. A084902, A077616, A276289.

Sequence in context: A244176 A038384 A038385 * A006239 A271560 A142040

Adjacent sequences: A084898 A084899 A084900 * A084902 A084903 A084904

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jun 10 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 | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 01:13 EST 2022. Contains 358453 sequences. (Running on oeis4.)