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

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A299276 Partial sums of A008137. 51
1, 5, 14, 31, 59, 101, 161, 242, 347, 479, 641, 837, 1070, 1343, 1659, 2021, 2433, 2898, 3419, 3999, 4641, 5349, 6126, 6975, 7899, 8901, 9985, 11154, 12411, 13759, 15201, 16741, 18382, 20127, 21979, 23941, 26017, 28210, 30523, 32959, 35521, 38213, 41038 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Euler transform of length 6 sequence [5, -1, 1, -1, 1, -1]. - Michael Somos, Oct 03 2018

LINKS

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

Index entries for linear recurrences with constant coefficients, signature (3,-3,1,0,1,-3,3,-1).

FORMULA

From Colin Barker, Feb 11 2018: (Start)

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

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) + a(n-5) - 3*a(n-6) + 3*a(n-7) - a(n-8) for n>7.

(End)

a(n) = -a(-1-n) for all n in Z.

EXAMPLE

G.f. = 1 + 5*x + 14*x^2 + 31*x^3 + 59*x^4 + 101*x^5 + 161*x^6 + ... - Michael Somos, Oct 03 2018

MATHEMATICA

a[ n_] := (8 n^3 + 12 n^2 + 40 n + 18 - {3, 3, 0, -3, -3, 3}[[Mod[n, 5] + 1]]) / 15; (* Michael Somos, Oct 03 2018 *)

PROG

(PARI) Vec((1 + x)^3*(1 - x + x^2)*(1 + x^2) / ((1 - x)^4*(1 + x + x^2 + x^3 + x^4)) + O(x^60)) \\ Colin Barker, Feb 11 2018

(PARI) {a(n) = (8*n^3 + 12*n^2 + 40*n + 18 - 3*(n%5<2) + 3*(n%5>2)) / 15}; /* Michael Somos, Oct 03 2018 */

CROSSREFS

Cf. A008137.

The 28 uniform 3D tilings: cab: A299266, A299267; crs: A299268, A299269; fcu: A005901, A005902; fee: A299259, A299265; flu-e: A299272, A299273; fst: A299258, A299264; hal: A299274, A299275; hcp: A007899, A007202; hex: A005897, A005898; kag: A299256, A299262; lta: A008137, A299276; pcu: A005899, A001845; pcu-i: A299277, A299278; reo: A299279, A299280; reo-e:  A299281, A299282; rho: A008137, A299276; sod: A005893, A005894; sve: A299255, A299261; svh: A299283, A299284; svj: A299254, A299260; svk: A010001, A063489; tca: A299285, A299286; tcd: A299287, A299288; tfs: A005899, A001845; tsi: A299289, A299290; ttw: A299257, A299263; ubt: A299291, A299292; bnn: A007899, A007202. See the Proserpio link in A299266 for overview.

Sequence in context: A070129 A081861 A299903 * A267167 A023652 A283523

Adjacent sequences:  A299273 A299274 A299275 * A299277 A299278 A299279

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Feb 10 2018

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 January 17 23:09 EST 2021. Contains 340249 sequences. (Running on oeis4.)