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A008413 Coordination sequence for 5-dimensional cubic lattice. 6
1, 10, 50, 170, 450, 1002, 1970, 3530, 5890, 9290, 14002, 20330, 28610, 39210, 52530, 69002, 89090, 113290, 142130, 176170, 216002, 262250, 315570, 376650, 446210, 525002, 613810, 713450, 824770, 948650, 1086002, 1237770, 1404930 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

If Y_i (i=1,2,3,4,5) are 2-blocks of a (n+5)-set X then a(n-4) is the number of 9-subsets of X intersecting each Y_i (i=1,2,3,4,5). - Milan Janjic, Oct 28 2007

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..10000

Milan Janjic, Two Enumerative Functions

Milan Janjić, On Restricted Ternary Words and Insets, arXiv:1905.04465 [math.CO], 2019.

J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf).

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).

FORMULA

G.f.: ((1+x)/(1-x))^5.

a(n) = (4/3)*n^4 + (20/3)*n^2 + 2 for n > 0. - Michael De Vlieger, Oct 04 2016

n*a(n) = 10*a(n-1) + (n-2)*a(n-2) for n > 1. - Seiichi Manyama, Jun 06 2018

MAPLE

4/3*n^4+20/3*n^2+2;

MATHEMATICA

LinearRecurrence[{5, -10, 10, -5, 1}, {1, 10, 50, 170, 450, 1002}, 40] (* Harvey P. Dale, May 02 2016 *)

{1}~Join~Table[4/3 n^4 + 20/3 n^2 + 2, {n, 32}] (* or *)

CoefficientList[Series[((1 + x)/(1 - x))^5, {x, 0, 32}], x] (* Michael De Vlieger, Oct 04 2016 *)

CROSSREFS

Sequence in context: A196507 A008531 A051230 * A006542 A237655 A261648

Adjacent sequences:  A008410 A008411 A008412 * A008414 A008415 A008416

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 27 12:22 EST 2020. Contains 332306 sequences. (Running on oeis4.)