A192836 Molecular topological indices of the pan graphs.

14, 29, 48, 83, 126, 193, 272, 383, 510, 677, 864, 1099, 1358, 1673, 2016, 2423, 2862, 3373, 3920, 4547, 5214, 5969, 6768, 7663, 8606, 9653, 10752, 11963, 13230, 14617, 16064, 17639, 19278, 21053, 22896, 24883, 26942, 29153, 31440, 33887, 36414, 39109, 41888

Offset

1,1

Comments

Pan graphs are defined for n >= 3; extended to n=1 using closed form.

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Molecular Topological Index

Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).

Formula

a(n) = (1/4)*(26 + 27*n + 4*n^2 + 2*n^3 + (-1)^n*(2+n)).

G.f. x*(14 + x - 24*x^2 + 14*x^3 + 14*x^4 - 7*x^5)/((1-x)^4*(1+x)^2). - Colin Barker, Aug 07 2012

E.g.f.: ((2-x)*exp(-x) - 28 + (26 + 33*x + 10*x^2 + 2*x^3)*exp(x))/4. - G. C. Greubel, Jan 04 2019

Maple

seq((1/4)*(26+27*n+4*n^2+2*n^3+(-1)^n*(2+n)), n=1..50); # Muniru A Asiru, Jan 05 2019

Mathematica

Table[(26+27*n+4*n^2+2*n^3+(-1)^n*(2+n))/4, {n, 1, 50)] (* G. C. Greubel, Jan 04 2019 *)

Prog

(PARI) Vec(-x*(7*x^5-14*x^4-14*x^3+24*x^2-x-14)/((x-1)^4*(x+1)^2) + O(x^50)) \\ Colin Barker, Jan 23 2017
(PARI) vector(50, n, (26+27*n+4*n^2+2*n^3+(-1)^n*(2+n))/4) \\ G. C. Greubel, Jan 04 2019
(Magma) [(26+27*n+4*n^2+2*n^3+(-1)^n*(2+n))/4: n in [1..50]]; // G. C. Greubel, Jan 04 2019
(Sage) [(26+27*n+4*n^2+2*n^3+(-1)^n*(2+n))/4 for n in (1..50)] # G. C. Greubel, Jan 04 2019
(GAP) List([1..50], n -> (26+27*n+4*n^2+2*n^3+(-1)^n*(2+n))/4); # G. C. Greubel, Jan 04 2019

Crossrefs

Sequence in context: A257645 A046045 A132756 * A124681 A195145 A263119

Adjacent sequences: A192833 A192834 A192835 * A192837 A192838 A192839

Keyword

nonn,easy

Author

Eric W. Weisstein, Jul 11 2011

Status

approved