A275908 Expansion of (1+2*x+4*x^2+4*x^3+6*x^4+4*x^5+x^6) / (1-3*x-x^2-6*x^3-7*x^4-7*x^5-5*x^6-x^7).

1, 5, 20, 75, 288, 1105, 4234, 16226, 62188, 238340, 913452, 3500857, 13417236, 51422337, 197079099, 755317101, 2894796675, 11094476468, 42520225774, 162961236161, 624558407329, 2393656389397, 9173827208656, 35159225871899, 134749776270503, 516436347919005, 1979272313718089

Offset

0,2

Links

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

T. Doslic, T. Short, Maximal matchings in polyspiro and benzenoid chains, arXiv:1511.00590, [math.CO], 2015. See Th. 4.4.

Index entries for linear recurrences with constant coefficients, signature (3,1,6,7,7,5,1).

Formula

a(n) = 3*a(n-1)+a(n-2)+6*a(n-3)+7*a(n-4)+7*a(n-5)+5*a(n-6)+a(n-7) for n>6. - Colin Barker, Aug 26 2016

Mathematica

CoefficientList[Series[(1+2x+4x^2+4x^3+6x^4+4x^5+x^6)/(1-3x-x^2-6x^3- 7x^4- 7x^5-5x^6-x^7), {x, 0, 30}], x] (* or *) LinearRecurrence[{3, 1, 6, 7, 7, 5, 1}, {1, 5, 20, 75, 288, 1105, 4234}, 30] (* Harvey P. Dale, Mar 08 2023 *)

Prog

(PARI) Vec((1+2*x+4*x^2+4*x^3+6*x^4+4*x^5+x^6)/(1-3*x-x^2-6*x^3- 7*x^4-7*x^5-5*x^6-x^7) + O(x^30)) \\ Colin Barker, Aug 26 2016

Crossrefs

Sequence in context: A000344 A290922 A275909 * A290909 A270023 A061278

Adjacent sequences: A275905 A275906 A275907 * A275909 A275910 A275911

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 26 2016

Status

approved