A110158 - OEIS

%I #21 Mar 12 2024 02:42:50

%S 0,0,0,0,1,3,10,26,69,173,436,1084,2699,6699,16634,41274,102425,

%T 254137,630584,1564600,3882103,9632247,23899510,59299318,147133173,

%U 365065973,905799668,2247464948,5576397299,13836125171

%N Expansion of x^4 / ((x+1)*(2*x^3-2*x^2-2*x+1)*(x-1)^2).

%C Floretion Algebra Multiplication Program, FAMP Code: 1jbasejcycsumseq[ + .5'k + .5k' + 'ij'], sumtype: (Y[15], *, vesy)

%H Colin Barker, <a href="/A110158/b110158.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-7,2,4,-2).

%F a(n) = -(-1)^n/4 + 7/4 - A077937(n) + A077937(n-1) + 4*A077937(n-2) - (n+1)/2. - _R. J. Mathar_, Nov 10 2009

%F a(n) = 3*a(n-1) + a(n-2) - 7*a(n-3) + 2*a(n-4) + 4*a(n-5) - 2*a(n-6) for n > 5. - _Colin Barker_, May 16 2019

%t CoefficientList[Series[x^4/((x+1)(2x^3-2x^2-2x+1)(x-1)^2),{x,0,30}],x] (* _Harvey P. Dale_, Jan 23 2019 *)

%o (PARI) concat([0,0,0,0], Vec(x^4 / ((1 - x)^2*(1 + x)*(1 - 2*x - 2*x^2 + 2*x^3)) + O(x^40))) \\ _Colin Barker_, May 16 2019

%Y Cf. A077847.

%K nonn,easy

%O 0,6

%A _Creighton Dement_, Sep 05 2005