A122745 Numbers of polypentagons with one internal vertex (see Cyvin et al. for precise definition).

1, 1, 2, 5, 12, 29, 72, 170, 404, 944, 2184, 5000, 11368, 25616, 57376, 127696, 282688, 622656, 1365472, 2982016, 6488320, 14068672, 30409216, 65536512, 140859776, 301990912, 645924864, 1378530048

Offset

3,3

Links

Table of n, a(n) for n=3..30.

S. J. Cyvin et al., Theory of polypentagons, J. Chem. Inf. Comput. Sci., 33 (1993), 466-474

Index entries for linear recurrences with constant coefficients, signature (6,-10,-2,12,4,8,-48,32).

Formula

G.f. x^3+x^4+2*x^5+12*x^6 -x^7 *(12 -43*x +18*x^2 +52*x^3 +18*x^4 -32*x^5 -176*x^6 +160*x^7) / ( (2*x^2-1) *(2*x^3-1) *(2*x-1)^3 ). - R. J. Mathar, Jul 26 2019

Maple

A122745 := proc(n)
    local a, d ;
    if n < 5 then
        1;
    else
        a := n-3 ;
        if modp(a, 3) = 0 then
            d := 1 ;
        else
            d := 0 ;
        end if;
        # note the typo in last exponent in (31b)
        (a+2)*(a+7)*2^(a-5)/3+2^floor(a/2-2) ;
        %+d*2^(floor((a-3)/3))/3 ;
    end if;
end proc:
seq(A122745(n), n=3..30) ; # R. J. Mathar, Jul 26 2019

Crossrefs

Sequence in context: A131710 A227237 A005593 * A166292 A010374 A307788

Adjacent sequences: A122742 A122743 A122744 * A122746 A122747 A122748

Keyword

nonn,easy

Author

N. J. A. Sloane, Sep 24 2006

Status

approved