A055806 a(n) = T(n,n-6), array T as in A055801.
1, 1, 1, 2, 3, 5, 8, 13, 21, 33, 53, 79, 125, 176, 273, 365, 554, 709, 1053, 1300, 1891, 2267, 3234, 3785, 5303, 6085, 8385, 9465, 12845, 14302, 19139, 21065, 27828, 30329, 39593, 42790, 55251, 59281, 75772, 80789, 102297, 108473, 136157, 143683, 178893
Offset: 6
Links
- G. C. Greubel, Table of n, a(n) for n = 6..1000
- Index entries for linear recurrences with constant coefficients, signature (1,6,-6,-15,15,20,-20,-15,15,6,-6,-1,1).
Programs
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GAP
Concatenation([1], List([7..50], n-> (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160 )); # G. C. Greubel, Jan 24 2020
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Magma
[1] cat [(48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160: n in [7..50]]; // G. C. Greubel, Jan 24 2020
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Maple
seq( `if(n=6,1, (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160), n=6..50); # G. C. Greubel, Jan 24 2020
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Mathematica
Table[If[n==6, 1, (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160], {n, 6,50}] (* G. C. Greubel, Jan 24 2020 *) -
PARI
vector(50, n, my(m=n+5); if(m==6, 1, (48915 -58884*m +29723*m^2 -7200*m^3 +965*m^4 -66*m^5 +2*m^6 + 3*(-1)^m*(-231345 +98988*m -18505*m^2 +1840*m^3 -95*m^4 +2*m^5))/92160)) \\ G. C. Greubel, Jan 24 2020
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Sage
[1]+[(48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160 for n in (7..50)] # G. C. Greubel, Jan 24 2020
Formula
From G. C. Greubel, Jan 24 2020: (Start)
a(n) = (48915 -58884*n +29723*n^2 -7200*n^3 +965*n^4 -66*n^5 +2*n^6 + 3*(-1)^n*(-231345 +98988*n -18505*n^2 +1840*n^3 -95*n^4 +2*n^5))/92160, n > 6.
G.f.: x^6*(1 -6*x^2 +x^3 +16*x^4 -4*x^5 -23*x^6 +8*x^7 +20*x^8 -8*x^9 -9*x^10 + 4*x^11 +2*x^12 -x^13)/((1-x)^7*(1+x)^6). (End)