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!)
A301451 Numbers congruent to {1, 7} mod 9. 4
1, 7, 10, 16, 19, 25, 28, 34, 37, 43, 46, 52, 55, 61, 64, 70, 73, 79, 82, 88, 91, 97, 100, 106, 109, 115, 118, 124, 127, 133, 136, 142, 145, 151, 154, 160, 163, 169, 172, 178, 181, 187, 190, 196, 199, 205, 208, 214, 217, 223, 226, 232, 235, 241, 244, 250, 253, 259, 262, 268 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First bisection of A056991, second bisection of A242660.

The squares of the terms of A174396 are the squares of this sequence.

LINKS

Colin Barker, Table of n, a(n) for n = 1..1000

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

FORMULA

O.g.f.: x*(1 + 6*x + 2*x^2)/((1 + x)*(1 - x)^2).

E.g.f.: (3 + 8*exp(x) - 11*exp(2*x) + 18*x*exp(2*x))*exp(-x)/4.

a(n) = a(n-1) + a(n-2) - a(n-3).

a(n) = 2*(2*n - 1) + (2*n - 3*(1 - (-1)^n))/4. Therefore, for n even a(n) = (9*n - 4)/2, otherwise a(n) = (9*n - 7)/2.

a(2n+1) = A017173(n). a(2n) = A017245(n-1). - R. J. Mathar, Feb 28 2019

MATHEMATICA

Table[2 (2 n - 1) + (2 n - 3 (1 - (-1)^n))/4, {n, 1, 60}]

PROG

(GAP) a := [1, 7, 10];; for n in [4..60] do a[n] := a[n-1] + a[n-2] - a[n-3]; od; a;

(Python) [2*(2*n-1)+(2*n-3*(1-(-1)**n))/4 for n in range(1, 70)]

(Sage) [n for n in (1..300) if n % 9 in (1, 7)]

(MAGMA) &cat [[9*n+1, 9*n+7]: n in [0..40]];

(PARI) Vec(x*(1 + 6*x + 2*x^2) / ((1 - x)^2*(1 + x)) + O(x^60)) \\ Colin Barker, Mar 22 2018

CROSSREFS

Cf. A274406: numbers congruent to {0, 8} mod 9.

Cf. A193910: numbers congruent to {2, 6} mod 9.

Subsequence of A016777, A026225, A029739, A033627, A047236, A047259, A055047, A055054, A056991, A153053, A187318, A242660.

Sequence in context: A083390 A234093 A287567 * A033817 A286873 A218128

Adjacent sequences:  A301448 A301449 A301450 * A301452 A301453 A301454

KEYWORD

nonn,easy

AUTHOR

Bruno Berselli, Mar 21 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 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)