cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A095671 Ninth column (m=8) of (1,4)-Pascal triangle A095666.

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%I A095671 #13 Aug 16 2015 12:03:57
%S A095671 4,33,153,525,1485,3663,8151,16731,32175,58630,102102,171054,277134,
%T A095671 436050,668610,1001946,1470942,2119887,3004375,4193475,5772195,
%U A095671 7844265,10535265,13996125,18407025,23981724,30972348,39674668,50433900
%N A095671 Ninth column (m=8) of (1,4)-Pascal triangle A095666.
%C A095671 If Y is a 4-subset of an n-set X then, for n>=11, a(n-11) is the number of 8-subsets of X having at most one element in common with Y. - _Milan Janjic_, Dec 08 2007
%H A095671 Harvey P. Dale, <a href="/A095671/b095671.txt">Table of n, a(n) for n = 0..1000</a>
%H A095671 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9, -36, 84, -126, 126, -84, 36, -9, 1).
%F A095671 G.f.: (4-3*x)/(1-x)^9.
%F A095671 a(n) = 4*b(n)-3*b(n-1) =(n+32)*binomial(n+7, 7)/8, with b(n):=binomial(n+8, 8)=A000581(n+8, 8).
%F A095671 a(0)=4, a(1)=33, a(2)=153, a(3)=525, a(4)=1485, a(5)=3663, a(6)=8151, a(7)=16731, a(8)=32175, a(n)=9*a(n-1)-36*a(n-2)+84*a(n-3)- 126*a(n-4)+ 126*a(n-5)-84*a(n-6)+36*a(n-7)-9*a(n-8)+a(n-9). - _Harvey P. Dale_, Jul 07 2015
%t A095671 CoefficientList[Series[(4-3x)/(1-x)^9,{x,0,30}],x] (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{4,33,153,525,1485,3663,8151,16731,32175},30] (* _Harvey P. Dale_, Jul 07 2015 *)
%o A095671 (Maxima) A095671(n):=(n+32)*binomial(n+7, 7)/8$
%o A095671 makelist(A095671(n),n,0,30); /* _Martin Ettl_, Nov 03 2012 */
%K A095671 nonn,easy
%O A095671 0,1
%A A095671 _Wolfdieter Lang_, Jun 11 2004