A227376 G.f.: 1/(1 - x - x^2 - x^3 + x^5 + x^6 + x^7).

1, 1, 2, 4, 7, 12, 21, 36, 62, 106, 181, 309, 527, 898, 1530, 2606, 4438, 7557, 12867, 21907, 37297, 63497, 108100, 184032, 313298, 533359, 907988, 1545751, 2631469, 4479778, 7626309, 12982911, 22101900, 37625912, 64053725, 109043981, 185634620, 316021206, 537989084, 915863373

Offset: 0

Author

Paul D. Hanna, Jul 09 2013

Keywords

• nonn
• easy

Comments

Compare to sequence A227375, generated by a continued fraction.

Lim_{n->infinity} a(n)/a(n+1) = 0.587411973105598587998520092901249815195963...

Examples

			G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 5*x^5 + 9*x^6 + 14*x^7 + 24*x^8 + ...
		

Links

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

Crossrefs

Cf. A227375.

Programs

Mathematica

CoefficientList[Series[1/(1-x-x^2-x^3+x^5+x^6+x^7),{x,0,50}],x] (* Harvey P. Dale, Mar 09 2021 *)

PARI

{a(n)=polcoeff(1/(1 - x - x^2 - x^3 + x^5 + x^6 + x^7 +x*O(x^n)),n)}
for(n=0,50,print1(a(n),", "))

Formula

a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-5) - a(n-6) - a(n-7). - Wesley Ivan Hurt, May 22 2021