A204631 Expansion of 1/(1 - x - x^2 + x^5 - x^7).

1, 1, 2, 3, 5, 7, 11, 17, 26, 40, 62, 96, 148, 229, 354, 547, 845, 1306, 2018, 3118, 4818, 7445, 11504, 17776, 27468, 42444, 65585, 101343, 156597, 241976, 373905, 577764, 892770, 1379522, 2131659, 3293873, 5089744, 7864752, 12152738, 18778601, 29016988

Offset: 0

Author

Roger L. Bagula, Jan 17 2012

Keywords

• nonn
• easy

Comments

Limiting ratio is 1.5452156..., the real root of x^7 - x^6 - x^5 + x^2 - 1.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Mohammed L. Nadji, Moussa Ahmia, Daniel F. Checa, and José L. Ramírez, Arndt Compositions with Restricted Parts, Palindromes, and Colored Variants, J. Int. Seq. (2025) Vol. 28, Issue 3, Article 25.3.6. See p. 8.
• Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,1).

Crossrefs

Cf. A029826, A117791, A143419, A143438, A143472, A143619, A143644, A147663, A173908, A173911, A173924, A173925, A174522, A175740, A175772, A175773, A175782, A181600, A225391, A225393, A225394, A225482, A225499.

Programs

Magma

m:=50; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/(1-x-x^2+x^5-x^7))); // G. C. Greubel, Nov 03 2018

Maple

seq(coeff(series(1/(1-x-x^2+x^5-x^7), x, n+1), x, n), n = 0..50); # G. C. Greubel, Mar 16 2020

Mathematica

CoefficientList[Series[1/(1 - x - x^2 + x^5 - x^7), {x, 0, 50}], x]
LinearRecurrence[{1,1,0,0,-1,0,1},{1,1,2,3,5,7,11},50] (* Harvey P. Dale, Aug 28 2013 *)

PARI

my(x='x+O('x^50)); Vec(1/(1-x-x^2+x^5-x^7)) \\ G. C. Greubel, Nov 16 2016

Formula

a(n) = a(n-1) + a(n-2) - a(n-5) + a(n-7). - Franck Maminirina Ramaharo, Nov 02 2018