A107548 Coordination sequence for B_15 lattice

1, 450, 37690, 1252106, 22905330, 272968658, 2350138410, 15679197210, 85233151458, 391856046050, 1567440920346, 5576512118570, 17955135189970, 53053662957042, 145495299159050, 373781033269306, 906487838507970, 2088730171811330, 4597733181281018

Offset

0,2

Links

Table of n, a(n) for n=0..18.

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

G.f.: -(x^15 + 4075*x^14 + 167181*x^13 + 2618655*x^12 + 20130045*x^11 + 84612255*x^10 + 206162985*x^9 + 300437235*x^8 + 265092435*x^7 + 141060465*x^6 + 44322135*x^5 + 7877805*x^4 + 733551*x^3 + 31045*x^2 + 435*x + 1) / (x - 1)^15. [Colin Barker, Nov 21 2012]

a(n) = 15*a(n-1)-105*a(n-2)+455*a(n-3)-1365*a(n-4)+3003*a(n-5)-5005*a(n-6)+6435*a(n-7)-6435*a(n-8)+5005*a(n-9)-3003*a(n-10)+1365*a(n-11)-455*a(n-12)+105*a(n-13)-15*a(n-14)+a(n-15). - Wesley Ivan Hurt, May 20 2021

Mathematica

LinearRecurrence[{15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1}, {1, 450, 37690, 1252106, 22905330, 272968658, 2350138410, 15679197210, 85233151458, 391856046050, 1567440920346, 5576512118570, 17955135189970, 53053662957042, 145495299159050, 373781033269306}, 20] (* Harvey P. Dale, Sep 21 2016 *)

Crossrefs

Sequence in context: A189653 A232035 A035752 * A263820 A269884 A145492

Adjacent sequences: A107545 A107546 A107547 * A107549 A107550 A107551

Keyword

nonn,easy

Author

N. J. A. Sloane, May 29 2005

Status

approved