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A sequence related to numeric partitions and Fermat Coefficients.
0

%I #8 Mar 30 2017 14:31:58

%S 1,1,5,15,44,99,217,429,811,1430,2438,3978,6312,9690,14550,21318,

%T 30669,43263,60115,82225,111044,148005,195143,254475,328759,420732,

%U 534076,672452,840656,1043460,1287036,1577532,1922745,2330445,2810385,3372291

%N A sequence related to numeric partitions and Fermat Coefficients.

%C The sequences m1^8, m2^4 and 6*m4^2 correspond to eight elements of a finite group of order eight belonging to the appropriate partition class.

%F Let m1^8 = A000580, m2^4 = 1 0 4 0 10 0 20 ... and let m4^2 = 1 0 0 0 2 0 0 0 3 0 0 0 4 ... Then a(n) = (1/8)*(m1^8 + m2^4 + 6*m4^2).

%F Empirical g.f.: x*(1 - 3*x + 5*x^2 + 3*x^3 - 4*x^4 + 3*x^5 + 5*x^6 - 3*x^7 + x^8) / ((1 - x)^8*(1 + x)^4*(1 + x^2)^2). - _Colin Barker_, Mar 30 2017

%e a(5)= 44 because (1/8)*( 330 + 10 + 12) = 352/8; a(9)= 811 because (1/8)*(6435 + 35 + 18) = 6488/8.

%Y Cf. A000041, A000292, A000580, A000973, A058936.

%K easy,nonn

%O 1,3

%A _Alford Arnold_, Jan 22 2001

%E More terms from _David Wasserman_, Jun 07 2002