|
|
A035841
|
|
Coordination sequence for A_15 lattice.
|
|
2
|
|
|
1, 240, 14520, 400080, 6447660, 70006512, 561075720, 3536846160, 18363363690, 81289041680, 315029394792, 1091144804400, 3433533723900, 9946019437200, 26808012135000, 67830161708592, 162298598439330, 369504358622640, 804648531335960, 1683493452034320
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
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 (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).
|
|
FORMULA
|
Sum_{d=1..15} C(16, d)*C(m/2-1, d-1)*C(15-d+m/2, m/2), where norm m is always even.
G.f.: -(x+1)*(x^14 + 224*x^13 + 10801*x^12 + 196224*x^11 + 1667001*x^10 + 7351008*x^9 + 17699017*x^8 + 23710208*x^7 + 17699017*x^6 + 7351008*x^5 + 1667001*x^4 + 196224*x^3 + 10801*x^2 + 224*x + 1) / (x-1)^15. - Colin Barker, Mar 03 2015
|
|
PROG
|
(PARI) Vec(-(x +1)*(x^14 +224*x^13 +10801*x^12 +196224*x^11 +1667001*x^10 +7351008*x^9 +17699017*x^8 +23710208*x^7 +17699017*x^6 +7351008*x^5 +1667001*x^4 +196224*x^3 +10801*x^2 +224*x +1) / (x -1)^15 + O(x^100)) \\ Colin Barker, Mar 03 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Joan Serra-Sagrista (jserra(AT)ccd.uab.es)
|
|
STATUS
|
approved
|
|
|
|