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A192830 Molecular topological indices of the halved cube graphs. 3
0, 4, 72, 672, 4800, 30240, 178752, 1017856, 5640192, 30528000, 161694720, 839393280, 4277944320, 21442011136, 105877094400, 515867934720, 2483703250944, 11831408197632, 55825060331520, 261152938393600, 1212257811824640, 5587829998485504 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Halved Cube Graph

Eric Weisstein's World of Mathematics, Molecular Topological Index

Index entries for linear recurrences with constant coefficients, signature (26,-296,1936,-8016,21792,-38912, 44032,-28672,8192).

FORMULA

a(n) = 2^(n-3)*n^2*(n-1)*(n-1+2^(n-2)). - Andrew Howroyd, May 11 2017

a(n) = 26*a(n-1) - 296*a(n-2) + 1936*a(n-3) - 8016*a(n-4) + 21792*a(n-5) - 38912*a(n-6) + 44032*a(n-7) - 28672*a(n-8) + 8192*a(n-9). - Eric W. Weisstein, May 27 2017

G.f.: 4*x^2*(1 - 8*x - 4*x^2 + 224*x^3 - 744*x^4 + 576*x^5 + 480*x^6)/((1-4*x)^4*(1-2*x)^5). - Eric W. Weisstein, May 27 2017

E.g.f.: x^2*(1 + 4*x + 2*x^2 + (1+2*x)*exp(2*x))*exp(2*x). - G. C. Greubel, Jan 04 2019

MATHEMATICA

Table[2^(-5+n)*(-1+n)*n^2*(-4 +2^n +4n), {n, 30}] (* Eric W. Weisstein, May 27 2017 *)

LinearRecurrence[{26, -296, 1936, -8016, 21792, -38912, 44032, -28672, 8192}, {0, 4, 72, 672, 4800, 30240, 178752, 1017856, 5640192}, 30] (* Eric W. Weisstein, May 27 2017 *)

Rest@CoefficientList[Series[(4x^2 (1-8x -4x^2 +224x^3 -744x^4 +576x^5 + 480 x^6)/((1-4x)^4 (1-2x)^5)), {x, 0, 30}], x] (* Eric W. Weisstein, May 27 2017 *)

PROG

(PARI) vector(30, n, 2^(n-3)*n^2*(n-1)*(n-1+2^(n-2))) \\ G. C. Greubel, Jan 04 2019

(Magma) [2^(n-3)*n^2*(n-1)*(n-1+2^(n-2)): n in [1..30]]; // G. C. Greubel, Jan 04 2019

(Sage) [2^(n-3)*n^2*(n-1)*(n-1+2^(n-2)) for n in (1..30)] # G. C. Greubel, Jan 04 2019

(GAP) List([1..30], n -> 2^(n-3)*n^2*(n-1)*(n-1+2^(n-2))); # G. C. Greubel, Jan 04 2019

CROSSREFS

Cf. A192831, A192826.

Sequence in context: A190398 A003752 A062018 * A119580 A209539 A139745

Adjacent sequences: A192827 A192828 A192829 * A192831 A192832 A192833

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jul 11 2011

EXTENSIONS

a(11)-a(22) from Andrew Howroyd, May 11 2017

STATUS

approved

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Last modified December 9 00:20 EST 2022. Contains 358698 sequences. (Running on oeis4.)