A224429 The Wiener index of the dendrimer D_1[n], defined pictorially in the A. R. Ashrafi et al. reference.

84, 18327, 233565, 1771209, 10839249, 59193537, 301745505, 1470068769, 6938902689, 32002414497, 145020899745, 648175476129, 2865160922529, 12550658135457, 54563037754785, 235694448080289, 1012548295652769, 4329277751424417, 18433454242526625

Offset

0,1

Comments

a(2) has been checked by the direct computation of the Wiener index (using Maple).

References

A. R. Ashrafi and H. Shabani, Computing Padmakar-Ivan index of four classes of dendrimers, Bulgarian Chem. Comm., 44, N0. 2, 2012, 127-130.

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (13,-64,148,-160,64).

Formula

a(n) = - 2655 + 26907*2^n + 16245*n*4^n -24168*4^n -570*n*2^n.

G.f. = 3(28+5745z+230z^2-34880z^3+20912z^4)/[(1-z)(1-2z)^2*(1-4z)^2].

Maple

a := proc (n) options operator, arrow: -2655+26907*2^n+16245*4^n*n-24168*4^n-570*2^n*n end proc: seq(a(n), n = 0 .. 18);

Mathematica

LinearRecurrence[{13, -64, 148, -160, 64}, {84, 18327, 233565, 1771209, 10839249}, 20] (* Harvey P. Dale, Feb 11 2025 *)

Crossrefs

Cf. A224430

Sequence in context: A278725 A186245 A377017 * A289325 A202923 A232914

Adjacent sequences: A224426 A224427 A224428 * A224430 A224431 A224432

Keyword

nonn,easy,changed

Author

Emeric Deutsch, Apr 06 2013

Status

approved