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
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jul 11 2011
STATUS
approved