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A187801 Pascal's triangle construction method applied to {1,1,2} as an initial term.

%I A187801 #29 Feb 16 2025 08:33:14
%S A187801 1,1,2,1,2,3,2,1,3,5,5,2,1,4,8,10,7,2,1,5,12,18,17,9,2,1,6,17,30,35,
%T A187801 26,11,2,1,7,23,47,65,61,37,13,2,1,8,30,70,112,126,98,50,15,2,1,9,38,
%U A187801 100,182,238,224,148,65,17,2,1,10,47,138,282,420,462,372
%N A187801 Pascal's triangle construction method applied to {1,1,2} as an initial term.
%C A187801 A neighborhood decomposition of triangle graph applied to each node gives three identical sequences (independent of start point) {1,3}.
%C A187801 For star graph (depend of start point) generated sequences are: one time {1,3} and three times {1,1,2}.
%C A187801 Triangle of expansion of (1+x+2*x^2)*(1+x)^n. - _Philippe Deléham_, Mar 10 2013
%H A187801 T. D. Noe, <a href="/A187801/b187801.txt">Rows n = 2..50 of triangle, flattened</a>
%H A187801 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/TriangleGraph.html">MathWorld: Triangle Graph</a>
%H A187801 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/StarGraph.html">MathWorld: Star Graph</a>
%F A187801 For the selection of the initial term: neighborhood decomposition of graph.
%F A187801 For sequence: Pascal's triangle construction method applied to selected initial term.
%F A187801 Row sums: A000079(n+2) = (4, 8, 16, 32, 64, ...). - _Philippe Deléham_, Mar 10 2013
%e A187801 Triangle begins:
%e A187801 1,1,2;
%e A187801 1,2,3,2;
%e A187801 1,3,5,5,2;
%e A187801 1,4,8,10,7,2;
%e A187801 1,5,12,18,17,9,2;
%e A187801 1,6,17,30,35,26,11,2;
%e A187801 1,7,23,47,65,61,37,13,2;
%e A187801 1,8,30,70,112,126,98,50,15,2;
%e A187801 1,9,38,100,182,238,224,148,65,17,2;
%e A187801 1,10,47,138,282,420,462,372,213,82,19,2;
%e A187801 1,11,57,185,420,702,882,834,585,295,101,21,2;
%e A187801 1,12,68,242,605,1122,1584,1716,1419,880,396,122,23,2;
%e A187801 1,13,80,310,847,1727,2706,3300,3135,2299,1276,518,145,25,2;
%e A187801 From _Philippe Deléham_, Mar 10 2013: (Start)
%e A187801 Row 2: 1+x+2*x^2
%e A187801 Row 3: (1+x+2*x^2)*(1+x) = 1+2*x+3*x^2+2*x^3
%e A187801 Row 4: (1+x+2*x^2)*(1+x)^2 = 1+3*x+5*x^2+5*x^3+2*x^4
%e A187801 Row 5: (1+x+2*x^2)*(1+x)^3 = 1+4*x+8*x^2+10*x^3+7*x^4+2*x^5
%e A187801 (End)
%t A187801 c = {1, 1, 2}; Join[{c}, t = Table[c = Append[c, 0]; c = c + RotateRight[c], {9}]]; Flatten[t] (* _T. D. Noe_, Mar 11 2013 *)
%Y A187801 Cf. A187801, A095660, A107232, A029635, A095660.
%K A187801 nonn,tabf
%O A187801 2,3
%A A187801 _Jakub Jaroslaw Ciaston_, Jan 06 2013