A079976 -id:A079976 - cp's OEIS frontend

A185265 a(0)=1, a(1)=2; thereafter a(n) = f(n-1) + f(n-2) where f() = A164387().

1, 2, 3, 6, 12, 22, 39, 70, 127, 231, 419, 759, 1375, 2492, 4517, 8187, 14838, 26892, 48739, 88335, 160099, 290164, 525894, 953132, 1727460, 3130855, 5674373, 10284254, 18639219, 33781788, 61226235, 110966650, 201116358, 364504015, 660628396, 1197325296, 2170036700, 3932982369, 7128151480

Offset: 0

N. J. A. Sloane, Mar 31 2011

Arises in studying lunar arithmetic.

G. C. Greubel, Table of n, a(n) for n = 0..1000
D. Applegate, M. LeBrun and N. J. A. Sloane, Dismal Arithmetic [Note: we have now changed the name from "dismal arithmetic" to "lunar arithmetic" - the old name was too depressing]
Index entries for linear recurrences with constant coefficients, signature (1,1,0,1,1).

Cf. A164387, A079976.

CoefficientList[Series[-(x + 1)*(x^4 + x^3 + 1)/(x^5 + x^4 + x^2 + x - 1), {x, 0, 50}], x] (* G. C. Greubel, Jun 25 2017 *)

x='x+O('x^50); Vec(-(x+1)*(x^4+x^3+1)/(x^5+x^4+x^2+x-1)) \\ G. C. Greubel, Jun 25 2017

Satisfies the same recurrence as A164387 and A079976, although with different initial conditions.
From Colin Barker, Jul 25 2013: (Start)
a(n) = a(n-1) + a(n-2) + a(n-4) + a(n-5) for n>5.
G.f.: -(x+1)*(x^4+x^3+1) / (x^5+x^4+x^2+x-1). (End)

A189101 Expansion of g.f. 1/(1-(x+x^2+x^3+x^4+x^6+x^7)).

Original entry on oeis.org

1, 1, 2, 4, 8, 15, 30, 59, 115, 225, 441, 863, 1689, 3307, 6474, 12673, 24809, 48567, 95075, 186120, 364352, 713261, 1396290, 2733399, 5350944, 10475089, 20506194, 40143239, 78585017, 153839228, 301158021, 589551538, 1154115087, 2259313307, 4422866209

Offset: 0

N. J. A. Sloane, Apr 19 2011

Compositions of n into parts !=5 and <=7. - Joerg Arndt, Jun 06 2011

Vincenzo Librandi, Table of n, a(n) for n = 0..300
D. Applegate, M. LeBrun, and N. J. A. Sloane, Dismal Arithmetic, J. Int. Seq. 14 (2011) # 11.9.8.
Index entries for linear recurrences with constant coefficients, signature (1,1,1,1,0,1,1).

This sequence is the next in the series after A000931, A006498, A079976, A079968.

makelist(coeff(taylor(1/(1-(x+x^2+x^3+x^4+x^6+x^7)), x, 0, n), x, n), n, 0, 34);  /* Bruno Berselli, Jun 05 2011 */

Vec(1/(1-(x+x^2+x^3+x^4+x^6+x^7))+O(x^99)) \\ Charles R Greathouse IV, Feb 26 2014

cp's OEIS Frontend

A185265 a(0)=1, a(1)=2; thereafter a(n) = f(n-1) + f(n-2) where f() = A164387().

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