A080957 Expansion of (5 - 9*x + 6*x^2)/(1-x)^4.

5, 11, 20, 34, 55, 85, 126, 180, 249, 335, 440, 566, 715, 889, 1090, 1320, 1581, 1875, 2204, 2570, 2975, 3421, 3910, 4444, 5025, 5655, 6336, 7070, 7859, 8705, 9610, 10576, 11605, 12699, 13860, 15090, 16391, 17765, 19214, 20740, 22345, 24031, 25800

Offset

0,1

Comments

Coefficient of x in the polynomial 6*(C(n,0) + C(n+1,1)x + C(n+2,2)x(x-1)/2 + C(n+3,3)x(x-1)(x-2)/6).

Links

Danny Rorabaugh, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = 3!(C(n+1, 1)-C(n+2, 2)/2+C(n+3, 3)/3) = (2n^3 + 3n^2 + 31n + 30)/6.

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n>3. - Vincenzo Librandi, Sep 07 2015

a(n+1) = a(n) + A117951(n+1), a(0) = 5. - Altug Alkan, Sep 28 2015

Mathematica

CoefficientList[Series[(5 - 9 x + 6 x^2)/(1 - x)^4, {x, 0, 45}], x] (* Vincenzo Librandi Sep 07 2015 *)
LinearRecurrence[{4, -6, 4, -1}, {5, 11, 20, 34}, 50] (* Harvey P. Dale, Dec 23 2018 *)

Prog

(PARI) Vec((5-9*x+6*x^2)/(1-x)^4 + O(x^60)) \\ Michel Marcus, Sep 06 2015
(Magma) [(2*n^3+3*n^2+31*n+30)/6: n in [0..50]]; // Vincenzo Librandi, Sep 07 2015
(PARI) a(n)=(2*n^3 + 3*n^2 + 31*n + 30)/6;
vector(40, n, a(n-1)) \\ Altug Alkan, Sep 28 2015

Crossrefs

Cf. A080956.

Sequence in context: A032527 A212978 A026038 * A118375 A225376 A099400

Adjacent sequences: A080954 A080955 A080956 * A080958 A080959 A080960

Keyword

easy,nonn

Author

Paul Barry, Mar 01 2003

Status

approved