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.

A132200 Numbers in (4,4)-Pascal triangle .

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%I A132200 #7 May 03 2021 20:13:56
%S A132200 1,4,4,4,8,4,4,12,12,4,4,16,24,16,4,4,20,40,40,20,4,4,24,60,80,60,24,
%T A132200 4,4,28,84,140,140,84,28,4,4,32,112,224,280,224,112,32,4,4,36,144,336,
%U A132200 504,504,336,144,36,4,4,40,180,480,840,1008,840,480,180,40,4
%N A132200 Numbers in (4,4)-Pascal triangle .
%C A132200 This triangle belongs to the family of (x,y)-Pascal triangles ; other triangles arise by choosing different values for (x,y): (1,1) -> A007318 ; (1,0) -> A071919 ; (3,2) -> A029618 ; (2,2) -> A134058 ; (-1,1) -> A112467 ; (0,1) -> A097805 ; (5,5) -> A135089 ; etc..
%H A132200 G. C. Greubel, <a href="/A132200/b132200.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A132200 T(n,k) = 4*binomial(n,k), n>0 ; T(0,0)=1.
%F A132200 Sum_{k=0..n} T(n,k) = 2^(n+2) - 3*[n=0]. - _G. C. Greubel_, May 03 2021
%e A132200 Triangle begins:
%e A132200   1;
%e A132200   4,  4;
%e A132200   4,  8,  4;
%e A132200   4, 12, 12,  4;
%e A132200   4, 16, 24, 16,  4;
%e A132200   4, 20, 40, 40, 20, 4;
%t A132200 Table[4*Binomial[n,k] -3*Boole[n==0], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, May 03 2021 *)
%o A132200 (Magma) [1] cat [4*Binomial(n,k): k in [0..n], n in [1..12]]; // _G. C. Greubel_, May 03 2021
%o A132200 (Sage)
%o A132200 def A132200(n,k): return 4*binomial(n,k) - 3*bool(n==0)
%o A132200 flatten([[A132200(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, May 03 2021
%Y A132200 Cf. A000079, A007318, A134058, A134059, A135089.
%K A132200 nonn,tabl
%O A132200 0,2
%A A132200 _Philippe Deléham_, Nov 19 2007