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A340459 a(n) is the sum of the numbers adjacent to n in a triangle in which the nonnegative integers are placed from top to bottom and from left to right.

%I A340459 #28 Mar 20 2021 23:29:24
%S A340459 3,9,10,18,26,23,31,44,50,40,48,68,74,80,61,69,98,104,110,116,86,94,
%T A340459 134,140,146,152,158,115,123,176,182,188,194,200,206,148,156,224,230,
%U A340459 236,242,248,254,260,185,193,278,284,290,296,302,308,314,320,226,234,338
%N A340459 a(n) is the sum of the numbers adjacent to n in a triangle in which the nonnegative integers are placed from top to bottom and from left to right.
%C A340459 The triangle of nonnegative integers begins:
%C A340459       0
%C A340459      1 2
%C A340459     3 4 5
%C A340459    6 7 8 9
%C A340459      ...
%e A340459 For n=4:
%e A340459 - the numbers adjacent to 4 are 1, 2, 3, 5, 7 and 8,
%e A340459 - so a(4) = 1 + 2 + 3 + 5 + 7 + 8 = 26.
%t A340459 T[i_,j_]:=Binomial[i+1,2]+j; a[i_,j_]:=If[j-1>=0,T[i,j-1],0]+If[i-1>=0&&j-1>=0, T[i-1,j-1],0]+If[i-1>=0&&j<=i-1,T[i-1,j],0]+If[j+1<=i,T[i,j+1],0]+T[i+1,j]+T[i+1,j+1]; Flatten[Table[a[i,j],{i,0,12},{j,0,i}]] (* _Stefano Spezia_, Jan 28 2021 *)
%Y A340459 Cf. A214177.
%K A340459 nonn
%O A340459 0,1
%A A340459 _Leonardo Sznajder_, Jan 10 2021
%E A340459 More terms from _Stefano Spezia_, Jan 28 2021