A330133 a(n) = (1/16)*(5 + (-1)^(1+n) - 4*cos(n*Pi/2) + 10*n^2).
0, 1, 3, 6, 10, 16, 23, 31, 40, 51, 63, 76, 90, 106, 123, 141, 160, 181, 203, 226, 250, 276, 303, 331, 360, 391, 423, 456, 490, 526, 563, 601, 640, 681, 723, 766, 810, 856, 903, 951, 1000, 1051, 1103, 1156, 1210, 1266, 1323, 1381, 1440, 1501, 1563, 1626, 1690, 1756
Offset: 0
Links
- Index entries for linear recurrences with constant coefficients, signature (2,-1,0,1,-2,1).
Programs
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Magma
I:=[0, 1, 3, 6, 10, 16]; [n le 6 select I[n] else 2*Self(n-1)-Self(n-2)+Self(n-4)-2*Self(n-5)+Self(n-6): n in [1..54]];
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Maple
gf:=(1/16)*(-exp(-x) + 5*exp(x)*(1 + 2*x + 2*x^2) - 4*cos(x)); ser := series(gf, x, 54): seq(factorial(n)*coeff(ser, x, n), n = 0 .. 53)
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Mathematica
Table[(1/16)*(5+(-1)^(1+n)-4*Cos[n*Pi/2]+10*n^2),{n,0,53}] LinearRecurrence[{2,-1,0,1,-2,1},{0,1,3,6,10,16},60] (* Harvey P. Dale, Jul 21 2021 *) -
PARI
concat([0], Vec(-x*(1 + x + x^2 + x^3 + x^4)/((-1 + x)^3*(1 + x)*(1 + x^2))+O(x^54)))
Formula
O.g.f.: -x*(1 + x + x^2 + x^3 + x^4)/((-1 + x)^3*(1 + x)*(1 + x^2)).
E.g.f.: (1/16)*(-exp(-x) + 5*exp(x)*(1 + 2*x + x^2) - 4*cos(x)).
a(n) = 2*a(n-1) - a(n-2) + a(n-4) -2*a(n-5) + a(n-6) for n > 5.
a(2*n-1) = A005891(n-1) for n > 0.
a(4*n) = 10*n^2. - Bernard Schott, Dec 06 2019
Comments