A082289 Expansion of x^4*(2+x)/((1+x)*(1-x)^5).

2, 9, 26, 59, 116, 206, 340, 530, 790, 1135, 1582, 2149, 2856, 3724, 4776, 6036, 7530, 9285, 11330, 13695, 16412, 19514, 23036, 27014, 31486, 36491, 42070, 48265, 55120, 62680, 70992, 80104, 90066, 100929, 112746, 125571, 139460, 154470

Offset: 4

Author

Michael Somos, Apr 07 2003

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 4..10000
• Index entries for two-way infinite sequences
• Index entries for linear recurrences with constant coefficients, signature (4,-5,0,5,-4,1).

Crossrefs

Cf. A070893, A082290.

Cf. A045947 (which contains the first differences). - Bruno Berselli, Aug 26 2011

Programs

Magma

[(1/96)*(2*(n-2)*n*(3*n^2-10*n+4)+3*(-1)^n-3): n in [4..50]]; // Vincenzo Librandi, Aug 29 2011

Mathematica

Drop[CoefficientList[Series[x^4(2+x)/((1+x)(1-x)^5),{x,0,50}],x],4] (* or *) LinearRecurrence[{4,-5,0,5,-4,1},{2,9,26,59,116,206},50] (* Harvey P. Dale, Aug 26 2013 *)

PARI

a(n)=polcoeff(if(n>0,x^4*(2+x)/((1+x)*(1-x)^5),x*(1+2*x)/((1+x)*(1-x)^5))+x*O(x^abs(n)),abs(n))

Formula

G.f.: x^4*(2+x)/((1+x)*(1-x)^5).

a(n) = 3*a(n-1) - 2*a(n-2) - 2*a(n-3) + 3*a(n-4) - a(n-5) + 3. If sequence is also defined for n <= 3 by this equation, then a(n)=0 for 0 <= n <= 3 and a(n) = A070893(-n) for n < 0.

a(n) = A082290(2*n-7).

a(n) = (1/96)*(2*(n-2)*n*(3*n^2 - 10*n + 4) + 3*(-1)^n - 3). a(n) - a(n-2) = A006002(n-3) for n > 5. - Bruno Berselli, Aug 26 2011

a(n) = 4*a(n-1) - 5*a(n-2) + 5*a(n-4) - 4*a(n-5) + a(n-6); a(4)=2, a(5)=9, a(6)=26, a(7)=59, a(8)=116, a(9)=206. - Harvey P. Dale, Aug 26 2013