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A245618 Triangle {H(n,k)} similar to Pascal's with sides of 1's, but interior entries are obtained by the rule: H(n,k) = |H(n-1,k)+(-1)^m(n,k)*H(n-1,k-1)|, where m(n,k) = H(n-1,k) + H(n-1,k-1).

%I A245618 #28 Nov 14 2014 13:02:56
%S A245618 1,1,1,1,2,1,1,1,1,1,1,2,2,2,1,1,1,4,4,1,1,1,2,3,8,3,2,1,1,1,1,5,5,1,
%T A245618 1,1,1,2,2,6,10,6,2,2,1,1,1,4,8,16,16,8,4,1,1,1,2,3,12,24,32,24,12,3,
%U A245618 2,1,1,1,1,9,36,56,56,36,9,1,1,1,1,2,2,10
%N A245618 Triangle {H(n,k)} similar to Pascal's with sides of 1's, but interior entries are obtained by the rule: H(n,k) = |H(n-1,k)+(-1)^m(n,k)*H(n-1,k-1)|, where m(n,k) = H(n-1,k) + H(n-1,k-1).
%C A245618 Let us consider the operation <+> over integers such that k<+>m = |k+(-1)^(k+m)*m|. Then H(n,k) = H(n-1,k)<+>H(n-1,k-1).
%C A245618 This is an analog of the formula binomial(n,k) = binomial(n-1,k) + binomial(n-1,k-1).
%H A245618 Peter J. C. Moses, <a href="/A245618/b245618.txt">First 50 rows.</a>
%e A245618 Triangle begins
%e A245618 1
%e A245618 1  1
%e A245618 1  2  1
%e A245618 1  1  1  1
%e A245618 1  2  2  2  1
%e A245618 1  1  4  4  1  1
%e A245618 1  2  3  8  3  2  1
%e A245618 ....................
%t A245618 parityAdd[a_, b_] := Abs[a + b (-1)^(a + b)];
%t A245618 triangleHP[n_, 0] := 1;
%t A245618 triangleHP[n_, n_] := 1;
%t A245618 triangleHP[n_, k_] := triangleHP[n, k] = parityAdd[triangleHP[n - 1, k - 1], triangleHP[n - 1, k]];
%t A245618 Flatten[Table[triangleHP[n, k], {n, 0, 15}, {k, 0, n}]] (* _Peter J. C. Moses_, Nov 05 2014 *)
%Y A245618 Cf. A007318, row sums in A245619, row "sums", using <+>, in A249388.
%K A245618 nonn,tabl
%O A245618 0,5
%A A245618 _Vladimir Shevelev_, Nov 05 2014
%E A245618 More terms from _Peter J. C. Moses_, Nov 05 2014