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.

A292767 Square array read by antidiagonals downwards: T(k,n) = sum of the site-perimeters of words of length n >= 1 over an alphabet of size k >= 1.

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%I A292767 #23 Aug 27 2019 06:06:42
%S A292767 4,6,10,8,28,18,10,72,74,28,12,176,281,152,40,14,416,1020,762,270,54,
%T A292767 16,960,3591,3664,1680,436,70,18,2176,12366,17120,10050,3238,658,88,
%U A292767 20,4864,41877,78336,58500,23160,5677,944,108,22,10752,139968,352768,333750,161352,47236,9276,1302,130
%N A292767 Square array read by antidiagonals downwards: T(k,n) = sum of the site-perimeters of words of length n >= 1 over an alphabet of size k >= 1.
%H A292767 Andrew Howroyd, <a href="/A292767/b292767.txt">Table of n, a(n) for n = 1..1275</a>
%H A292767 Aubrey Blecher, Charlotte Brennan, Arnold Knopfmacher, and Toufik Mansour, <a href="http://dx.doi.org/10.22108/toc.2017.21465">The Site-Perimeter of Words</a>, Transactions on Combinatorics, Vol. 6 No. 2 (2017), pp. 37-48. ISSN (print): 2251-8657, ISSN (on-line): 2251-8665.
%F A292767 G.f. of row k: k*x*(36 + 12*k + (8 - 24*k - 8*k^2)*x + (2 - 5*k + 4*k^2 - k^3)*x^2)/(12*(1 - k*x)^2). - _Andrew Howroyd_, Oct 27 2018
%e A292767 Array begins (rows are indexed by k = 1,2,3,4,...; columns by n = 1,2,3,4,...):
%e A292767    4,   6,    8,    10,     12,      14,       16, ...
%e A292767   10,  28,   72,   176,    416,     960,     2176, ...
%e A292767   18,  74,  281,  1020,   3591,   12366,    41877, ...
%e A292767   28, 152,  762,  3664,  17120,   78336,   352768, ...
%e A292767   40, 270, 1680, 10050,  58500,  333750,  1875000, ...
%e A292767   54, 436, 3238, 23160, 161352, 1102464,  7420896, ...
%e A292767   70, 658, 5677, 47236, 383131, 3049270, 23916361, ...
%e A292767   ...
%t A292767 RowGf[k_] := k x (36 + 12k + (8 - 24k - 8k^2) x + (2 - 5k + 4k^2 - k^3) x^2)/(12(1 - k x)^2);
%t A292767 T[k_, n_] := SeriesCoefficient[RowGf[k], {x, 0, n}];
%t A292767 Table[T[k - n + 1, n], {k, 1, 10}, {n, k, 1, -1}] // Flatten (* _Jean-François Alcover_, Aug 27 2019, from PARI *)
%o A292767 (PARI)
%o A292767 RowGf(k) = {k*x*(36 + 12*k + (8 - 24*k - 8*k^2)*x + (2 - 5*k + 4*k^2 - k^3)*x^2)/(12*(1 - k*x)^2)}
%o A292767 M(k,n)={Mat(vectorv(k,k,Vec(RowGf(k) + O(x*x^n))))}
%o A292767 { M(10,8) } \\ _Andrew Howroyd_, Oct 27 2018
%Y A292767 Row k=2 is A128135.
%K A292767 nonn,tabl
%O A292767 1,1
%A A292767 _N. J. A. Sloane_, Sep 27 2017
%E A292767 Terms a(16) and beyond from _Andrew Howroyd_, Oct 27 2018