A117486 Expansion of 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))^2.
1, 2, 5, 10, 20, 34, 59, 94, 149, 224, 334, 480, 685, 950, 1307, 1762, 2357, 3100, 4050, 5220, 6685, 8466, 10659, 13294, 16494, 20298, 24859, 30234, 36609, 44056, 52806, 62952, 74770, 88380, 104112, 122116, 142786, 166304, 193134, 223504, 257954, 296756, 340544
Offset: 0
Links
- Colin Barker, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,1,-2,-1,-4,4,4,2,0,-10,0,2,4,4,-4,-1,-2,1,2,-1).
- Index entries for two-way infinite sequences
Crossrefs
Programs
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Magma
n:=4; G:=SymmetricGroup(n); H:=DirectProduct(G,G); MolienSeries(H);
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Mathematica
CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3)(1-x^4))^2,{x,0,50}],x] (* Harvey P. Dale, Jul 22 2012 *) -
Maxima
a(n):=floor(2*floor(-n/3)*cos(2*%pi*(n+1)/3)/81+(n+2)*cos(%pi*n/ 2)/128+(n+1)*(2835*(n^2+29*n+246)*(-1)^n+6*n^6+414*n^5+11556*n^4 +166944*n^3 +1320045*n^2+5489625*n+10008110)/ 17418240+1/2); /* Tani Akinari, Nov 14 2012 */
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PARI
Vec(1 / ((1 - x)^8*(1 + x)^4*(1 + x^2)^2*(1 + x + x^2)^2) + O(x^40)) \\ Colin Barker, Apr 07 2019
Formula
G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4))^2.
a(n) = 2*a(n-1) + a(n-2) - 2*a(n-3) - a(n-4) - 4*a(n-5) + 4*a(n-6) + 4*a(n-7) + 2*a(n-8) - 10*a(n-10) + 2*a(n-12) + 4*a(n-13) + 4*a(n-14) - 4*a(n-15) - a(n-16) - 2*a(n-17) + a(n-18) + 2*a(n-19) - a(n-20) for n>19. - Colin Barker, Apr 07 2019
Extensions
Entry revised by N. J. A. Sloane, Mar 10 2007
Comments