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A192836 Molecular topological indices of the pan graphs. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 22 22:24 EDT 2020. Contains 337291 sequences. (Running on oeis4.)