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A053539 a(n) = n * 8^(n-1). 5
0, 1, 16, 192, 2048, 20480, 196608, 1835008, 16777216, 150994944, 1342177280, 11811160064, 103079215104, 893353197568, 7696581394432, 65970697666560, 562949953421312, 4785074604081152, 40532396646334464, 342273571680157696 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The Szeged index of the hypercube Q_n (see the Ashrafi et al. reference (p. 45, last line). - Emeric Deutsch, Aug 06 2014

REFERENCES

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

A. R. Ashrafi, B. Manoochehrian, H. Yousefi-Azari, On Szeged polynomial of a graph, Bull. Iranian Math. Soc., 33, 2007, 37-46. - Emeric Deutsch, Aug 06 2014

F. Ellermann, Illustration of binomial transforms

Index entries for linear recurrences with constant coefficients, signature (16,-64).

FORMULA

a(n) = 16*a(n-1) - 64*a(n-2), with a(0)=0, a(1)=1. - Emeric Deutsch, Aug 06 2014

From G. C. Greubel, May 16 2019: (Start)

G.f.: x/(1-8*x)^2.

E.g.f.: x*exp(8*x). (End)

MAPLE

a := proc(n) option remember; if n<2 then n else 16*a(n-1)-64*a(n-2) end if end proc: seq(a(n), n = 0 .. 20); # Emeric Deutsch, Aug 06 2014

MATHEMATICA

Table[n 8^(n-1), {n, 0, 20}] (* or *) LinearRecurrence[{16, -64}, {0, 1}, 20] (* Harvey P. Dale, Feb 01 2017 *)

PROG

(MAGMA) [n*8^(n-1): n in [0..20]]; // Vincenzo Librandi, Feb 09 2011

(PARI) a(n) = n*8^(n-1); \\ Joerg Arndt, Aug 07 2014

(Sage) [n*8^(n-1) for n in (0..20)] # G. C. Greubel, May 16 2019

(GAP) List([0..20], n-> n*8^(n-1)) # G. C. Greubel, May 16 2019

CROSSREFS

Binomial transform of A027473.

Cf. A001787, A053464, A053469, A053540.

Sequence in context: A071081 A317601 A000767 * A218176 A120994 A016178

Adjacent sequences:  A053536 A053537 A053538 * A053540 A053541 A053542

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jan 15 2000

EXTENSIONS

Offset corrected and name edited by Emeric Deutsch, Aug 06 2014

STATUS

approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)