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%I A355802 #13 Jul 19 2022 10:43:31
%S A355802 1,1,1,1,2,1,1,2,2,1,1,2,2,2,1,1,2,3,3,2,1,1,2,3,4,3,2,1,1,2,3,4,4,3,
%T A355802 2,1,1,2,3,5,6,5,3,2,1,1,2,3,5,7,7,5,3,2,1,1,2,3,5,7,8,7,5,3,2,1,1,2,
%U A355802 3,5,8,11,11,8,5,3,2,1,1,2,3,5,8,12,14,12,8,5,3,2,1
%N A355802 A variant of Pascal's triangle (A007318) where new rows are added cyclically below, to the right and to the left.
%C A355802 The procedure to build the present triangle is as follows:
%C A355802 - row 0 contains a single 1:
%C A355802 .           1
%C A355802 - row 1 is added below, each new term is the sum of the adjacent prior terms:
%C A355802 .           1
%C A355802 .          ---
%C A355802 .         1   1
%C A355802 - row 2 is added to the right, each new term is the sum of the adjacent prior terms:
%C A355802 .           1
%C A355802 .          \
%C A355802 .         1 \ 2
%C A355802 .            \
%C A355802 .       1   1 \ 1
%C A355802 - row 3 is added to the left, each new term is the sum of the adjacent prior terms:
%C A355802 .           1
%C A355802 .            /
%C A355802 .         2 / 1
%C A355802 .          /
%C A355802 .       2 / 1   2
%C A355802 .        /
%C A355802 .     1 / 1   1   1
%C A355802 - row 4 is added below, each new term is the sum of the adjacent prior terms:
%C A355802 .          1
%C A355802 .
%C A355802 .        2   1
%C A355802 .
%C A355802 .      2   1   2
%C A355802 .
%C A355802 .    1   1   1   1
%C A355802 .   ---------------
%C A355802 .  1   2   2   2   1
%C A355802 - and so on.
%H A355802 Rémy Sigrist, <a href="/A355802/b355802.txt">Table of n, a(n) for n = 0..10010</a>
%H A355802 Rémy Sigrist, <a href="/A355802/a355802.png">Illustration of the odd terms among the first 2^9 rows</a>
%H A355802 Rémy Sigrist, <a href="/A355802/a355802.gp.txt">PARI program</a>
%H A355802 <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%F A355802 T(n, 0) = T(n, n) = 1.
%F A355802 T(n, k) = T(n, n-k).
%e A355802 Triangle begins:
%e A355802     1;
%e A355802     1, 1;
%e A355802     1, 2, 1;
%e A355802     1, 2, 2, 1;
%e A355802     1, 2, 2, 2, 1;
%e A355802     1, 2, 3, 3, 2, 1;
%e A355802     1, 2, 3, 4, 3, 2, 1;
%e A355802     1, 2, 3, 4, 4, 3, 2, 1;
%e A355802     1, 2, 3, 5, 6, 5, 3, 2, 1;
%e A355802     1, 2, 3, 5, 7, 7, 5, 3, 2, 1;
%e A355802     1, 2, 3, 5, 7, 8, 7, 5, 3, 2, 1;
%e A355802     1, 2, 3, 5, 8, 11, 11, 8, 5, 3, 2, 1;
%e A355802     1, 2, 3, 5, 8, 12, 14, 12, 8, 5, 3, 2, 1;
%e A355802     ...
%o A355802 (PARI) See Links section.
%Y A355802 Cf. A007318, A355806.
%K A355802 nonn,tabl
%O A355802 0,5
%A A355802 _Rémy Sigrist_, Jul 17 2022

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