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%I #27 Apr 08 2024 15:37:31
%S 1,1,1,2,2,2,3,3,4,5,5,6,7,7,8,9,10,11,12,13,14,15,16,17,19,20,21,23,
%T 24,25,27,28,30,32,33,35,37,38,40,42,44,46,48,50,52,54,56,58,61,63,65,
%U 68,70,72,75,77,80,83,85,88,91,93,96,99,102,105,108,111
%N Expansion of 1/((1-x)*(1-x^3)*(1-x^8)).
%C Mark Underwood observed that the number of partitions into four nonzero squares of the squares of primes is given by A025428(A001248(n)) = a(prime(n)-4), cf. sequence A216374. - _M. F. Hasler_, Sep 16 2012
%C a(n) is the number of partitions of n into parts 1, 3, and 8. - _Joerg Arndt_, Apr 05 2024
%C a(n) = a(-12-n) for all n in Z using the floor definition. - _Michael Somos_, Apr 04 2024
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1,0,0,0,1,-1,0,-1,1).
%F a(n) = floor((x^2+12x+c)/48) with 51 <= c <= 58. - _M. F. Hasler_, Sep 16 2012
%F a(0)=1, a(1)=1, a(2)=1, a(3)=2, a(4)=2, a(5)=2, a(6)=3, a(7)=3, a(8)=4, a(9)=5, a(10)=5, a(11)=6, a(n)=a(n-1)+a(n-3)-a(n-4)+a(n-8)-a(n-9)- a(n-11)+ a(n-12). - _Harvey P. Dale_, Nov 29 2012
%e G.f. = 1 + x + x^2 + 2*x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 3*x^7 + 4*x^8 + 5*x^9 + ... - _Michael Somos_, Apr 04 2024
%t CoefficientList[Series[1/((1-x)(1-x^3)(1-x^8)),{x,0,60}],x] (* or *) LinearRecurrence[{1,0,1,-1,0,0,0,1,-1,0,-1,1},{1,1,1,2,2,2,3,3,4,5,5,6},60] (* _Harvey P. Dale_, Nov 29 2012 *)
%t a[ n_] := Floor[((n+6)^2/16 + 1)/3]; (* _Michael Somos_, Apr 04 2024 *)
%o (PARI) A025769(n)=((n+6)^2+16)\48 \\ _M. F. Hasler_, Sep 16 2012
%K nonn,easy
%O 0,4
%A _N. J. A. Sloane_
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