A323270 Expansion of x*(1-x)*(3-13*x+24*x^2-17*x^3-18*x^4+35*x^5-3*x^6-14*x^7+x^9) / (1-7*x+20*x^2-30*x^3+16*x^4+20*x^5-32*x^6+6*x^7+11*x^8-2*x^9-x^10).

0, 3, 5, 12, 33, 92, 257, 715, 1988, 5529, 15377, 42745, 118775, 330015, 917059, 2548644, 7083187, 19684909, 54704928, 152026360, 422489498, 1174129226, 3262989670, 9068054805, 25200655379, 70034119048, 194629155239, 540886699852, 1503158050714, 4177369402390, 11609167438104, 32262594620909

Offset

0,2

Links

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

K. A. Van'kov, V. M. Zhuravlyov, Regular tilings and generating functions, Mat. Pros. Ser. 3, issue 22, 2018 (127-157) [in Russian]. See Theorem 3.

Index entries for linear recurrences with constant coefficients, signature (7,-20,30,-16,-20,32,-6,-11,2,1).

Formula

a(n) = 7*a(n-1) - 20*a(n-2) + 30*a(n-3) - 16*a(n-4) - 20*a(n-5) + 32*a(n-6) - 6*a(n-7) - 11*a(n-8) + 2*a(n-9) + a(n-10). - Colin Barker, Jan 10 2019

Mathematica

CoefficientList[Series[x(1-x)(3-13x+24x^2-17x^3-18x^4+35x^5- 3x^6- 14x^7+ x^9) / (1-7x+20x^2-30x^3+16x^4+20x^5-32x^6+ 6x^7+ 11x^8-2x^9-x^10), {x, 0, 50}], x] (* or *) LinearRecurrence[{7, -20, 30, -16, -20, 32, -6, -11, 2, 1}, {0, 3, 5, 12, 33, 92, 257, 715, 1988, 5529, 15377, 42745}, 40] (* Harvey P. Dale, Mar 06 2023 *)

Prog

(PARI) concat(0, Vec(x*(1 - x)*(3 - 13*x + 24*x^2 - 17*x^3 - 18*x^4 + 35*x^5 - 3*x^6 - 14*x^7 + x^9) / (1 - 7*x + 20*x^2 - 30*x^3 + 16*x^4 + 20*x^5 - 32*x^6 + 6*x^7 + 11*x^8 - 2*x^9 - x^10) + O(x^40))) \\ Colin Barker, Jan 10 2019

Crossrefs

Sequence in context: A046091 A002905 A220832 * A087610 A243013 A191636

Adjacent sequences: A323267 A323268 A323269 * A323271 A323272 A323273

Keyword

nonn,easy

Author

N. J. A. Sloane, Jan 09 2019

Status

approved