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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A301926 a(n+3) = a(n) + 24*n + 32, a(0)=0, a(1)=3, a(2)=13. 1
0, 3, 13, 32, 59, 93, 136, 187, 245, 312, 387, 469, 560, 659, 765, 880, 1003, 1133, 1272, 1419, 1573, 1736, 1907, 2085, 2272, 2467, 2669, 2880, 3099, 3325, 3560, 3803, 4053, 4312, 4579, 4853, 5136, 5427, 5725 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Difference table:

0,  3, 13, 32, 59, 93, 136, 187, ...

3, 10, 19, 27, 34, 43,  51, ... = b(n)

7,  9,  8,  7,  9,  8, ... .

The sequence of last decimal digits of a(n) has period 15 and contain no 1's, 4's or 8's.

a(n) is e(n), hexasection, in A262397(n-1).

b(n) mod 9 is of period 9: 3, 1, 1, 0, 7, 7, 6, 4, 4.

LINKS

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

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

FORMULA

a(-n) = A262997(n).

a(n) = 2*a(n-1) - a(n-2) + a(n-3) - 2*a(n-4) + a(n-5).

Trisections: a(3n) = 4*n*(9*n-1), a(3n+1) = 3 + 20*n + 36*n^2, a(3n+2) = 13 + 44*n + 36*n^2.

a(n+15) = a(n) + 40*(22+3*n).

G.f.: x*(1 + x)*(3 + 4*x + 5*x^2) / ((1 - x)^3*(1 + x + x^2)). - Colin Barker, Jun 20 2018

MATHEMATICA

CoefficientList[ Series[ -x (5^3 +9x^2 +7x +3)/(x -1)^3 (x^2 +x +1), {x, 0, 40}], x] (* or *)LinearRecurrence[{2, -1, 1, -2, 1}, {0, 3, 13, 32, 59, 93}, 41] (* Robert G. Wilson v, Jun 20 2018 *)

PROG

(PARI) concat(0, Vec(x*(1 + x)*(3 + 4*x + 5*x^2) / ((1 - x)^3*(1 + x + x^2)) + O(x^40))) \\ Colin Barker, Jun 20 2018

CROSSREFS

Cf. A262997, A262397. A000290, A240438, A016754, A262523 (hexasections). Cf. A130518.

Sequence in context: A052493 A279068 A247216 * A211800 A218922 A061938

Adjacent sequences:  A301923 A301924 A301925 * A301927 A301928 A301929

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jun 20 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 March 29 20:20 EDT 2020. Contains 333117 sequences. (Running on oeis4.)