A025769 Expansion of 1/((1-x)*(1-x^3)*(1-x^8)).

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, 24, 25, 27, 28, 30, 32, 33, 35, 37, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 61, 63, 65, 68, 70, 72, 75, 77, 80, 83, 85, 88, 91, 93, 96, 99, 102, 105, 108, 111

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

a(n) is the number of partitions of n into parts 1, 3, and 8. - Joerg Arndt, Apr 05 2024

a(n) = a(-12-n) for all n in Z using the floor definition. - Michael Somos, Apr 04 2024

Examples

			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
		

Links

• Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1,0,0,0,1,-1,0,-1,1).

Programs

Mathematica

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 *)
a[ n_] := Floor[((n+6)^2/16 + 1)/3]; (* Michael Somos, Apr 04 2024 *)

PARI

A025769(n)=((n+6)^2+16)\48  \\ M. F. Hasler, Sep 16 2012

Formula

a(n) = floor((x^2+12x+c)/48) with 51 <= c <= 58. - M. F. Hasler, Sep 16 2012

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